Power supply device and method for controlling power supply device

ABSTRACT

Provided is multi-phase interleaving control in a power supply device, the control allowing the pulse widths ΔT of respective phases to overlap one another, so as to be adaptable to wideband pulse power control. In applying dead beat control to the multi-phase interleaving, constant current control is performed using combined current of the respective phase current values, and the pulse widths ΔT(k) is computed under this constant current control, thereby preventing variation of the pulse widths ΔT(k) between the phases, and achieving stable power control. Accordingly, the pulse power control becomes adaptable to wideband. Furthermore, wideband control is possible also in two-level pulse power control that performs control by switching at high frequency between High-level power and Low-level power.

TECHNICAL FIELD

The present invention relates to a power supply device and a method forcontrolling the power supply device.

BACKGROUND ART

With a proliferation of denser and more precise thin films generated bya process such as ashing and etching, manufacturing equipment such assemiconductor manufacturing equipment and flat-panel manufacturingequipment are demanded to have a function for supplying pulse-state RFpower to a plasma load. In particular, it is being demanded to performtwo-level pulse power control, i.e., wideband High/Low pulse poweroperation with a system where RF power is continuously variable,switched between “Low power” being minimum power that keeps plasma frombeing extinguished and “High power” that is required for generating thinfilms.

A frequency band required by the High/Low pulse power operation is from1 Hz to 50 kHz, for example. There are known some power supply devicesfor providing RF power, which employ class-A to class-E amplifiers usingPI control. However, with the PI control, it is impossible to achievethe two-level pulse power control covering the wideband of several totens of kHz.

Under these circumstances, a power supply used in a field of RF powersources for equipment is demanded to have capability of two-level pulsepower control that performs wideband High/Low pulse power control.

As power supplies promising rapid response, a power supply employing aninterleaving system is provided, and for example, there are known thearts as described in the following patent documents 1 to 3.

In the patent document 1, there is described that aninterleaving-control power supply device is provided for performingpower factor correction (PFC), including a master converter and a slaveconverter, for operating a switching element in the master converter anda switching element in the slave converter, with a predetermined phasedifference, and interleaved voltage control is performed based on theoutput voltage being fed back.

In the patent document 2, there is described that a step-up choppercircuit comprises an interleaving circuit of multi-phase control typewith n phases at least two, where a main switch performs switchingoperations with a predetermined phase difference mutually, andinterleaving control is performed based on the output voltage being fedback.

In the patent document 3, there is described to solve a problem ofcurrent imbalance between phases, occurring in a converter withmulti-phase interleaving system, and thereby protecting power elements,and interleaved current control is performed based on phase currentvalues of sub-circuits provided for respective phases.

PRIOR ART DOCUMENT Patent Document

Patent Document 1

Japanese Unexamined Patent Application Publication No. 2010-119285

Patent Document 2

Japanese Unexamined Patent Application Publication No. 2015-177636

Patent Document 3

Japanese Unexamined Patent Application Publication No. 2015-220976

Patent Document 4

Japanese Patent No. 5704772

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

It can be considered to apply multi-phase interleaving to a power supplydevice to provide wideband pulse power control. The interleaving controldisclosed in the aforementioned patent documents 1 and 2 is a controlsystem where voltage is controlled based on the output voltage being fedback, and the patent document 3 discloses a control system where currentis controlled based on the phase current values of the respectivephases. In those disclosed arts, there are problems as the following.

The interleaving control disclosed in the patent documents 1 and 2 isconstant voltage control that is performed based on the feedback ofoutput voltage vo, and thus there is a problem that secondaryoscillating voltage may occur in a step response, causing overshoot orundershoot of the output voltage. In order to prevent such overshoot andundershoot, it is necessary to provide a setting of a low-speed controlresponse, thus failing to address a rapid response.

FIG. 19 shows an equivalent circuit of an LCR circuit, illustrating theconstant voltage control for feeding back the output voltage vo. Thisfigure illustrates an example of the power supply device that includes astep-down chopper circuit comprising the LCR circuit.

In the LCR circuit as shown in FIG. 19, the output voltage vo given bythe step response is expressed by the following formula, where the inputvoltage is U:

$\begin{matrix}{{v_{O}(s)} = {{\frac{\frac{R}{1 + {sCR}}}{{{sL}/3} + \begin{matrix}R \\{1 + {sCR}}\end{matrix}}\frac{U}{s}} = {{\frac{\frac{3}{LC}}{s^{2} + {\begin{matrix}1 \\{CR}\end{matrix}s} + \begin{matrix}3 \\{LC}\end{matrix}}\frac{U}{s}} = {\frac{\omega_{n}^{2}}{s^{2} + {2\;{\varsigma\omega}_{n}s} + \omega_{n}^{2}}\frac{U}{s}}}}} & (1)\end{matrix}$

The formula 1 above indicates that the output voltage vo is secondaryoscillating voltage, and also indicates occurrence of overshoot orundershoot.

The interleaving control described in the patent document 3 is currentcontrol performed based on the phase current values of respectivephases. Therefore, there is a problem that more than one detector isrequired to detect the respective phase values, and further there isanother problem that this may give rise to complexity in control.

Furthermore, in the conventional interleaving control, there is aproblem regarding a set width of the pulse width ΔT(k) per phase for theinterleaving, and it is difficult to be adapted to wideband.

If the bandwidth of the pulse power control has to support the wideband,the set width of the pulse width ΔT(k) per phase for the interleaving isrequired to be freely adjustable. However, in the conventionalinterleaving control, the pulse widths of the respective phases are notsupposed to overlap one another, and there are limits imposed on the setwidth ΔT(k).

By way of example, the interleaving control described in the patentdocument 1 is two-phase interleaving having an opposite phaserelationship, and the patent document 2 does not disclose theinterleaving control where the pulse widths of the respective phasesoverlap one another. The interleaving control as described in the patentdocument 3 is to allocate the pulses per phase at predetermined phaseintervals in time series, as shown in FIG. 4 of the patent document 3,and it is the control where the pulse widths of the respective phases donot overlap one another.

Therefore, when the conventionally known interleaving control isapplied, limits are imposed on the control so that the pulse widths ΔTof the respective phases do not overlap one another, and thus mutualoverlapping of the pulse widths ΔT of the respective phases in theinterleaving is not permitted. Therefore, the pulse width ΔT is notadjustable to have any set width, and it is difficult for the pulsepower control to be adaptable to the wideband.

Therefore, in the multi-phase interleaving control of the power supplydevice, the control is required where the pulse widths ΔT of therespective phases are allowed to overlap one another, so as to beadaptable to the wideband pulse power control.

An objective of the present invention is to solve the aforementionedconventional problems, and to provide the multi-phase interleavingcontrol of the power supply device, the control allowing the pulsewidths ΔT of the respective interleaving phases to overlap one another,so as to be adaptable to the wideband pulse power control.

Means for Solving the Problems

As a control system, there is known a dead beat control that can expectmore rapid dynamic response and higher gain, relative to the PI control.According to the dead beat control, a pulse width ΔT(k) is computed inevery sampling cycle in a manner that an output of the (k+1)^(th)sampling cycle becomes equal to a target value in a state equationobtained by discrete model development of a circuit state assuminginputs and outputs as state variables, and switching operation iscontrolled by thus obtained pulse width ΔT(k).

Power control in a power supply device where dead beat control isapplied to multi-phase interleaving is not yet known. If it is attemptedto apply the dead beat control to the multi-phase interleaving perphase, stable power control cannot be expected, since the pulse widthΔT(k) being obtained by the dead beat control per phase may vary betweenphases.

According to the present invention, constant current control isperformed by using combined current of respective phase current values,when the dead beat control is applied to the multi-phase interleaving,and the pulse width ΔT(k) is computed in this constant current control,thereby preventing variation of the pulse width ΔT(k) between phases andachieving stable power control.

According to the present invention, the constant current control isperformed using the combined current of the respective phase currentvalues, enabling the control using the pulse width ΔT(k) that allows thepulse widths of the respective phases to overlap one another, and thepulse power control becomes adaptable to wideband. In addition,two-level pulse power control that performs control by switching betweenHigh-level power and Low-level power at high frequencies is also madeadaptable to wideband control.

(Power Supply Device)

The power supply device of the present invention includes an LC choppercircuit, provided with a controller for performing step response controlto follow a command value according to multi-phase interleaving controlthat performs multi-phase control using a plurality of phase currentvalues, and a switching signal generator for generating a switchingsignal.

The controller computes the pulse width ΔT(k) of the switching signalfor driving the LC chopper circuit, in every sampling cycle T, accordingto the constant current control (dead beat control) in a predeterminedcycle, the constant current control being performed on the basis of thecontrol current including combined current that is obtained by combiningthe phase current values in the LC chopper circuit.

The switching signal generator of the present invention generates aswitching signal per phase, using the pulse width ΔT(k) computed by thecontroller as the pulse width ΔT(k) per phase current.

In the computation of the pulse width ΔT(k), it is based on the controlcurrent including the combined current that is obtained by combiningphase current values, whereby the limits imposed to avoid overlaps ofthe pulse widths ΔT(k) of the respective phases can be eliminated,enabling obtainment of the pulse width ΔT(k) allowing the pulse widthsΔT of the respective phases to overlap one another, so as to beadaptable to the wideband pulse power control.

In addition, according to the computation based on the control currentincluding the combined current obtained by combining the phase currentvalues, the needs for multiple detectors can be eliminated, which areconfigured to detect the respective phase current values.

The controller performs the constant current control in a predeterminedcycle, using the pulse width ΔT(k) computed in an operation part, as thepulse widths ΔT(k) of the respective phase current values. The constantcurrent control using the control current may prevent secondaryoscillating voltage of output voltage in a step response.

(Method for Controlling Power Supply Device)

The method for controlling the power supply device of the presentinvention is a control method of the power supply device including theLC chopper circuit, and this is a control method for giving a stepresponse to follow a command value, according to multi-phaseinterleaving control that performs multi-phase control using a pluralityof phase current values.

The control method comprises a control step and a switching signalgeneration step. The control step performs a computation of the pulsewidth ΔT(k) of the switching signal for driving the LC chopper circuit,in every sampling cycle T, according to the constant current control(dead beat control) in a predetermined cycle, which is performed on thebasis of the control current including the combined current obtained bycombining phase current values in the LC chopper circuit.

The switching signal generation step generates a switching signal perphase, using thus computed pulse width ΔT(k) as the pulse width ΔT(k)per phase current. The LC chopper circuit performs the switchingoperation with the pulse width ΔT(k) in every cycle, thereby performingthe dead beat control to follow a command value, being command voltageor command current.

In the power supply device and the method for controlling the powersupply device of the present invention, the constant current controlusing the control current may include the constant current control usingcombined current of inductance current values of the respective phasesin the LC circuit, the constant current control using capacitancecurrent, and a combination of the constant current control using thecombined current of inductance current values and the constant currentcontrol using the capacitance current.

The constant current control using the combined current of inductancecurrent values gives the step response of output voltage that followsthe command voltage.

The capacitance current is obtained by subtracting load current from thecombined current of the inductance current values. The constant currentcontrol using the capacitance current gives the step response of thecapacitance current that follows the command current.

The constant current control using the combined current of inductancecurrent values and the constant current control using the capacitancecurrent gives a combination of constant current control including afirst step response allowing the capacitance current to follow thecommand current by the constant current control using the capacitancecurrent, and a second step response allowing the output voltage tofollow the command voltage by the constant current control using thecombined current of the inductance current values.

(Control Current)

(a) Common Part

One mode of the control current of the present invention relates to theconstant current control using as the control current, the combinedcurrent of inductance current values of the respective phases in the LCcircuit, and on the basis of this control current, inductancecurrent-based constant current control or capacitance current-basedconstant current control is performed.

For the case of three-phase interleaving control in the multi-phaseinterleaving control, the per-phase pulse width ΔT(k) of the switchingoperation in the LC circuit is expressed by:

${\Delta\;{T(k)}} = {\frac{1}{V_{i\; n}(k)}\left\{ {{\frac{L}{3}{i_{L}\left( {k + 1} \right)}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right){i_{L}(k)}} + {{Tv}_{O}(k)} - {\frac{T^{2}}{2C}{i_{R}(k)}}} \right\}}$where Vin(k) is input voltage, vo(k) is output voltage, iL(k) iscombined current of inductance current values of respective phases,iR(k) is load current, L is inductance of the LC circuit, C iscapacitance of the LC circuit, and T is sampling cycle period.

The constant current control according to the combined current iL(k) ofthe inductance current gives the step response of the output voltagevo(k) that follows the command voltage VREF.

(b) (Mode1)

One mode of the control current of the present invention relates to theconstant current control based on the capacitance current of the LCcircuit.

For the case of three-phase interleaving control in the multi-phaseinterleaving control, per-phase pulse width ΔT(k) of the switchingoperation in the LC circuit is expressed by:

${\Delta\;{T(k)}} = \frac{{\frac{L}{3}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right){i_{C}(k)}} + {{Tv}_{O}(k)}}{V_{i\; n}(k)}$where Vin(k) is input voltage, vo(k) is output voltage, ic(k) iscapacitance current, IC-REF is capacitance command current, L isinductance of the LC circuit, C is capacitance of the LC circuit, and Tis sampling cycle period.

The constant current control using the capacitance current ic(k)according to this mode gives the step response allowing the capacitancecurrent ic(k) to follow the capacitance command current IC-REF.According to this mode, the load current iR(k) and the inductancecurrent iL(k) can be removed from the expression of the pulse widthGT(k).

(c) (Mode2)

One mode of the control current of the present invention relates to theconstant current control based on the capacitance current in the LCcircuit.

For the case of three-phase interleaving control in the multi-phaseinterleaving control, per-phase pulse width ΔT(k) of the switchingoperation in the LC circuit is expressed by:

${\Delta\;{T(k)}} = \frac{{\frac{L}{3}\beta_{2}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right)I_{C\text{-}{REF}}} + {TV}_{C\; 1}}{V_{i\; n}(k)}$where Vin(k) is input voltage, vc1 is initial value of output voltage,IC-REF is capacitance command current, β2 is a factor of the capacitancecommand current, L is inductance of the LC circuit, C is capacitance ofthe LC circuit, and T is sampling cycle period.

The constant current control using the capacitance current ic(k)according to this mode gives the step response that allows thecapacitance current ic(k) to follow the capacitance command currentIC-REF, using Vc1 as an initial value of the output voltage. In thisconstant current control, the capacitance command current is given byβ2·IC-REF.

(d) (Mode3)

One mode of the control current of the present invention relates to theconstant current control according to the inductance current in the LCcircuit.

For the case of three-phase interleaving control in the multi-phaseinterleaving control, per-phase pulse width ΔT(k) of the switchingoperation in the LC circuit is expressed by:

${\Delta\;{T(k)}} = {\frac{1}{V_{i\; n}(k)}{\frac{L}{3}\left\lbrack {{A_{V}V_{REF}} - {\left( {1 - \beta_{3} - \frac{3T^{2}}{2{LC}}} \right){i_{C}(k)}} + {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}}} \right\rbrack}}$where Vin(k) is input voltage, VREF is command voltage, vo(k) is outputvoltage, ic(k) is capacitance current, Av is a factor by which adifference (VREF−vo(k)) between the command voltage VREF and the outputvoltage vo(k) is multiplied, β3 is a factor of capacitance current, L isinductance of the LC circuit, C is capacitance of the LC circuit, and Tis sampling cycle period.

The constant current control using the inductance current iL(k)according to this mode maybe represented as the constant current controlusing the capacitance current ic(k), by replacing the inductance currentiL(k) with the capacitance current ic(k). According to this mode, thepulse width ΔT(k) can be computed by using the capacitance current ic(k)and the output voltage vo(k) as the feedback signals.

(e) (Mode3)

One mode of the control current of the present invention relates to theconstant current control based on the inductance current in the LCcircuit.

For the case of three-phase interleaving control in the multi-phaseinterleaving control, the per-phase pulse width ΔT(k) of the switchingoperation in the LC circuit is expressed by:

${\Delta\;{T(k)}} = {\frac{V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)L}{3T} - \frac{T}{2C}} \right\}{i_{C}(k)}}}{V_{i\; n}(k)}T}$where Vin(k) is input voltage, VREF is command voltage, ic(k) iscapacitance current, β3 is a factor of capacitance current, L isinductance of the LC circuit, C is capacitance of the LC circuit, and Tis one cycle period.

In the constant current control using the inductance current iL(k)according to this mode, Av is set to 3T/L in the mode of (d). Setting Avto this value, the pulse width ΔT(k) is computed by using only thecapacitance current ic(k) as the feedback signal without using theoutput voltage vo(k).

(Control Mode)

One mode of the control for the power supply device of the presentinvention is a two-level dead beat control by a two-way step-downchopper circuit employing multi-phase interleaving without using PIcontrol.

In the interleaving method, the number of phases n is set to establishmulti-phase, whereby the switching frequency becomes n-times higher thana drive switching frequency, thereby achieving n-times more controlresponse, and in addition, for a smoothing capacitor, a valuecorresponding to the switching frequency n-times higher than the driveswitching frequency is employed. Accordingly, drastic reduction involume of the smoothing capacitor can be expected.

In general, a detector for detecting a DC signal is slow in responsespeed, whereas an AC transformer for detecting an AC signal can respondrapidly. Therefore, according to the mode of the present invention wherecapacitance current is used as the control current in the power supplydevice of the present invention, AC signals of the capacitance currentcan be detected rapidly, thereby enabling rapid response in the deadbeat control, even though DC signals including other AC components aredetected at a relatively low speed.

In addition, according to an aspect of the present invention, theconstant current control can prevent overshoot and undershoot of thestep response.

Furthermore, according to an aspect of the present invention, since thecontrol current is combined current of the inductance current values ofrespective phases, it is possible to reduce the number of detectors fordetecting feedback signals being the control current.

There are known class-A to class-E amplifiers as amplifiers to controlthe RF power by converting the previous stage DC voltage to AC voltage,with the use of an inverter in the LC chopper circuit. Among thoseamplifiers, the class-A to class-C amplifiers control RF power by adropper system, and therefore, conversion efficiencies of RF power areapproximately from 30% and 50%. On the other hand, the class-D amplifierand the class-E amplifier control the RF power with varying the DCvoltage on the previous stage by using the switching system, and thushigh conversion efficiencies of the RF power, from 90% to 93%, can beobtained at a typical high frequency of 13.56 MHz.

Therefore, in the dead beat control according to multi-phaseinterleaving in the power supply device of the present invention, theclass-D amplifier and the class-E amplifier are suitable as amplifiersto which the switching control is applicable.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a schematic configuration of a powersupply device according to the present invention

FIG. 2 illustrates examples of pulse width ΔT(k) for the case of phasecurrent controlled by the power supply device according to the presentinvention;

FIG. 3 illustrates an example of inductance current control by the powersupply device according to the present invention;

FIG. 4 illustrates an example of capacitance current control by thepower supply device according to the present invention;

FIG. 5 illustrates an example of the inductance current control and thecapacitance current control by the power supply device according to thepresent invention;

FIG. 6 illustrates one mode of the inductance current control and thecapacitance current control the power supply device according to thepresent invention:

FIG. 7 illustrates one mode of the inductance current control and thecapacitance current control by the power supply device according to thepresent invention;

FIG. 8 illustrates examples of the inductance current control and thecapacitance current control by the power supply device according to thepresent invention;

FIG. 9 is a flowchart showing output voltage settling to command voltageaccording to mode1 to mode3;

FIG. 10 illustrates an example of a chopper circuit in the power supplydevice according to the present invention;

FIG. 11 illustrates an LCR circuit in the power supply device accordingto the present invention;

FIG. 12 illustrates an equivalent circuit of the LCR circuit in thepower supply device according to the present invention;

FIG. 13 illustrates a first order transfer function of the constantvoltage control;

FIG. 14 illustrates a second order transfer function of the constantvoltage control;

FIG. 15 illustrates an example for controlling all RF generator to whichthe power supply device of the present invention is applied;

FIG. 16 is a flowchart showing an example for controlling the RFgenerator to which the power supply device of the present invention isapplied;

FIG. 17 is a flowchart showing an example of High/Low control inequipment to which the power supply device of the present invention isapplied;

FIG. 18 illustrates a control example of a DC power supply device and anAC power supply device to which the power supply device of the presentinvention is applied; and

FIG. 19 illustrates the constant voltage control for feedback of theoutput voltage vo.

BEST MODE FOR CARRYING OUT THE INVENTION

There will now be described a power supply device and a method forcontrolling the power supply device of the present invention, withreference to the accompanying drawings FIGS. 1 to 18. With reference toFIG. 1, a schematic configuration of the power supply device of thepresent invention will be described, and with reference to FIGS. 2 to 9,an example for controlling the power supply device of the presentinvention will be described. With reference to FIGS. 10 to 12,derivation of the pulse width ΔT(k) of the present invention will bedescribed, and with reference to FIGS. 13 and 14, followability to acommand value will be described. With reference to FIGS. 15 to 18,application examples of the power supply device of the present inventionwill be described.

(Schematic Configuration of the Power Supply Device of the PresentInvention)

With reference to FIG. 1, a schematic configuration of the power supplydevice of the present invention will be described. The power supplydevice 1 of the present invention comprises an LC chopper circuit 2configured to receive input voltage Vin and to deliver output voltage voand load current iR, a switching signal generator 5 configured togenerate a switching signal for controlling ON/OFF operations of aswitching element in the LC chopper circuit 2, and a controller 6configured to input feedback signals from the LC chopper circuit 2 and aload, computing a pulse width ΔT(k), and to output thus computed pulsewidth ΔT(k) to the switching signal generator 5.

The LC chopper circuit 2 comprises an LC circuit 4 includingseries-parallel connection of inductance L and capacitance C, and aswitching circuit 3 configured to provide the LC circuit 4 withinductance current iL formed by performing multi-phase switching controlon the input voltage Vin.

The controller 6 computes the pulse width ΔT(k) of the switching signalfor controlling ON/OFF operations of the switching element in theswitching circuit 3. The pulse width ΔT(k) determines a time width ofthe ON state of the switching element in one cycle of switching, andcontrols power supplied to the load through the LC circuit 4, based onthe length of the pulse width ΔT(k). By way of example, assuming thetime width of the switching cycle as T, the pulse width ΔT(k) withrespect to the time width T is represented in the form of duty ratio.

The controller 6 computes the pulse width ΔT(k) as to each samplingcycle, so that an output of the (k+1)^(th) sampling cycle may become atarget value, and performs the dead beat control for controlling theswitching operation according to thus obtained pulse width ΔT(k). Thecontroller 6 performs, in the dead beat control, constant currentcontrol in a predetermined cycle based on the control current includingcombined current obtained by combining phase current values within theLC chopper circuit 2, and further computes the pulse width ΔT(k) of theswitching signal for driving the switching element (not illustrated) ofthe switching circuit 3 in the LC chopper circuit 2, every samplingcycle T.

The controller 6 sets the pulse width ΔT(k) computed by the constantcurrent control using the control current including the combinedcurrent, as the pulse width ΔT(k) per phase current. The constantcurrent control using the control current may prevent secondaryoscillating voltage of output voltage in the step response.

The switching signal generator 5 of the present invention generates aper-phase switching signal, setting the pulse width ΔT(k) computed bythe controller 6, as the pulse width ΔT(k) of the per-phase current. Thepulse width ΔT(k) is computed on the basis of the control currentincluding the combined current that is obtained by combining the phasecurrent values. In this computation, since the control current is basedon the combined current of the phase current values, restrictions causedby overlapping between the pulse widths ΔT(k) of the respective phasescan be eliminated. Therefore, it is possible to obtain the pulse widthΔT(k) where the pulse widths ΔT of the respective phases are allowed tooverlap one another.

FIG. 2 illustrates an example of the pulse width ΔT(k) for the case ofthree-phase current. FIG. 2(a) illustrates an example where the pulsewidths ΔT(k) of phase current of the three phases overlap one another,with respect to the time width T in one cycle of switching. FIG. 2(b)illustrates an example where the pulse widths ΔT(k) of the current oftwo phases out of the three phases overlap one another, with respect tothe time width T in one cycle of switching. FIG. 2(c) illustrates anexample where the pulse widths ΔT(k) of phase current of the threephases do not overlap.

When the switching operation is performed in the switching circuit 3according to n-phase multi-phase interleaving, inductance currents iL1to iLn flow respectively through n inductances L (L1 to Ln) in the LCchopper circuit 2. The controller 6 receives inputs, as the constantcurrent, the current including the combined current iL that is obtainedby combining the respective phase current values corresponding to theinductance currents iL1 to iLn.

As the control current, capacitance current ic may also be used, whichis obtained by subtracting load current iR from the combined current iL,instead of the combined current IL obtained by combining the inductancecurrent of the respective phase current.

(Constant Current Control)

The constant current control according to the controller 6 includes aplurality of control modes. Those control modes include, a mode ofinductance current control, a mode of capacitance current control, and acontrol mode combining the inductance current control and thecapacitance current control.

With reference to FIGS. 3 to 8, there will now be described the multiplemodes of constant current control, and the pulse width ΔT(k) in each ofthe control modes.

(Modes of Constant Current Control and Pulse Width ΔT(k))

In the LCR circuit comprising the LC chopper circuit 2 in FIG. 1, whichis connected to the load 7, inductance current iL of the inductance L orthe capacitance current ic of the capacitance C in the LC choppercircuit is used as the control current to perform the constant currentcontrol. The inductance current iL(t), the capacitance current ic(t),and the output voltage vo(t) are expressed by the following formula 2,respectively:

$\begin{matrix}{{{i_{L}(t)} = {{{i_{C}(t)} + {i_{R}(t)}} = {{A_{V}\left\{ {V_{REF} - {v_{O}(t)}} \right\}} + {\beta\;{i_{C}(t)}} + {i_{R}(t)}}}}{{i_{C}(t)} = {{\frac{A_{V}}{1 - \beta}\left\{ {V_{REF} - {v_{O}(t)}} \right\}} = {C\frac{d}{dt}{v_{O}(t)}}}}{{v_{O}(t)} = {V_{REF}\left\{ {1 - e^{{- \frac{A_{V}}{{({1 - \beta})}C}}t}} \right\}}}} & (2)\end{matrix}$

In the multi-phase interleaving, the inductance current iL(t) in theformula 2 above is combined current obtained by combining the inductancecurrent values iL1 to iLn of the respective phases of n inductances L(L1 to Ln), included in the LC chopper circuit. There is a relationshipof iL(t)=ic(t)+iR(t) between the inductance current iL(t) and thecapacitance current ic. Here, iR(t) represents load current of the loadR.

In the three-phase interleaving control as an example of the multi-phaseinterleaving control, the pulse width ΔT(k) when the constant currentcontrol is performed, using the aforementioned inductance current andthe capacitance current as the control current, is expressed by thefollowing formula 3:

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{1}{V_{i\; n}(k)}\left\{ {{\frac{L}{3}{i_{L}\left( {k + 1} \right)}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right){i_{L}(k)}} + {{Tv}_{O}(k)} - {\frac{T^{2}}{2C}{i_{R}(k)}}} \right\}}} & (3)\end{matrix}$where Vin(k) is input voltage, vo(k) is output voltage, iL(k) iscombined current of inductance current values of respective phases,iR(k) is load current, L is inductance of the LC circuit, C iscapacitance of the LC circuit, and T is the sampling cycle.

The constant current control may be either the inductance current-basedconstant current control where the inductance current is used as thecontrol current, or the capacitance current-based constant currentcontrol where the capacitance current is used as the control current.

There will now be described each of the constant current control modes,the mode of inductance current-based constant current control, the modeof capacitance current-based constant current control, and the controlmode combining the inductance current-based constant current control andthe capacitance current-based constant current control. In here,three-phase interleaving control will be described as an example of themulti-phase interleaving control.

(Mode of Inductance Current-Based Constant Current Control)

FIG. 3 schematically illustrates the modes of the inductance currentcontrol performed by the controller, FIGS. 3(a) and 3(b) illustrateschematic configurations of the control mode, FIG. 3(c) shows an exampleof the command voltage VREF, and FIG. 3(d) shows an example of theoutput voltage vo.

FIG. 3 illustrates two configuration examples of the inductancecurrent-based constant current control, taking the three-phaseinterleaving control as an example. The inductance current-basedconstant current control performs current control, so that a differencemay become zero between the inductance current and a rated current valueor a value obtained by multiplying the rated current value by apredefined factor.

In the configuration of FIG. 3(a), according to the mode of inductancecurrent-based constant current control of the three-phase interleavingcontrol, the pulse width ΔT(k) expressed by the following formula 4 isused, and with the use of the capacitance current ic(k) and the outputvoltage vo(k) being fed back, the step response control is performed sothat the output voltage vo(k) may become equal to the command voltageVREF.

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{1}{V_{i\; n}(k)}{\frac{L}{3}\left\lbrack {{A_{V}V_{REF}} - {\left( {1 - \beta_{3} - \frac{3T^{2}}{2{LC}}} \right){i_{C}(k)}} + {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}}} \right\rbrack}}} & (4)\end{matrix}$

In the configuration of FIG. 3(b), according to the mode of inductancecurrent-based constant current control of the three-phase interleavingcontrol, the pulse width ΔT(k) expressed by the following formula 5 isused, and with the use of the capacitance current ic(k) being fed back,the step response control is performed so that the output voltage vo(k)may become the command voltage VREF. In this configuration, by settingthe factor Av as Av=3T/L, feedback of the output voltage vo(k) becomesunnecessary, and thus only the capacitance current ic(k) is detected andfed back, to determine the pulse width ΔT(k):

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)L}{3T} - \frac{T}{2C}} \right\}{i_{C}(k)}}}{V_{i\; n}(k)}T}} & (5)\end{matrix}$

The command voltage VREF as shown in FIG. 3(c) illustrates an example oftwo-level command voltage, High level VH and Low level VL in the H/Ltwo-level control, and the output voltage vo as shown in FIG. 3(d)illustrates an example of the two-level step response.

The voltage waveforms in FIGS. 3(c) and 3(d) are schematically shown forthe illustration purpose, not indicating actual voltage waveforms.

(Mode of Capacitance Current-Based Constant Current Control)

FIG. 4 schematically illustrates an example of three-phase interleavingcontrol for the mode of the capacitance current control according to thecontroller, FIG. 4(a) illustrates a schematic configuration, FIG. 4(b)illustrates an example of the command current IC-REF of the capacitancecurrent, and FIG. 4(c) shows the capacitance current ic.

In the configuration of FIG. 4(a), according to the mode of capacitancecurrent-based constant current control in the three-phase interleavingcontrol, the pulse width ΔT(k) expressed by the following formula 6 isused, and with the use of the capacitance current ic(k) and the outputvoltage vo(k) being fed back, the step response control is performed sothat the capacitance current may become equal to the capacitance commandcurrent IC-REF.

$\begin{matrix}{{\Delta\;{T(k)}} = \frac{{\frac{L}{3}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right){i_{C}(k)}} + {{Tv}_{O}(k)}}{V_{i\; n}(k)}} & (6)\end{matrix}$

The command current IC-REF of the capacitance current as shown in FIG.4(b) includes an example of two-level command current; IC-REFHcorresponding to High level VH, and IC-REFL corresponding to Low levelVL in H/L two-level control, and the capacitance current is as Shown inFIG. 4(c) indicates an example of two-level step response.

The voltage waveforms as shown in FIGS. 4(b) and 4C are schematicallyshown for the illustration purpose, not indicating actual voltagewaveforms.

(Control Mode Combining the Inductance Current-Based Constant CurrentControl and the Capacitance Current-Based Constant Current Control)

The constant current control of the present invention is furtherprovided with a mode for performing the step response control accordingto the multi-stage constant current control mode including thecapacitance current-based constant current control, and the inductancecurrent-based constant current control performed subsequently, inaddition to the mode of the inductance current-based constant currentcontrol, and the mode of capacitance current-based constant currentcontrol.

This multi-stage control mode includes a first control mode forperforming the inductance current-based constant current control afterperforming the capacitance current-based constant current control, and asecond control mode for performing two-stage capacitance current-basedconstant current control, and subsequently the inductance current-basedconstant current control is performed.

FIGS. 5 to 7 illustrate the control mode combining the inductancecurrent-based constant current control and the capacitance current-basedconstant current control. FIG. 5(a) schematically illustrates thecontroller and FIG. 5(b) illustrates the command voltage VREF.

In the control mode combining the capacitance current-based constantcurrent control and the inductance current-based constant currentcontrol, FIGS. 6(a) and 6(b) illustrate the command current IC-REF andthe output voltage vo in the first control mode. FIGS. 7(a) and 7(b)illustrate the command current IC-REF and the output voltage vo in thesecond control mode when the capacitance current-based constant currentcontrol is performed in two stages, mode1 and mode2, and thereafter, theinductance current-based constant current control is performed in mode3.

(First Control Mode)

In the control mode combining the capacitance current-based constantcurrent control and the inductance current-based constant currentcontrol, for the case of the first control mode, the capacitancecurrent-based constant current control is performed in the first-stage.When the output voltage vo reaches the switching voltage Vc, it isswitched to the inductance current-based constant current control in thesecond stage, and then, the constant current control is performed tofollow the command voltage VREF.

In the first-stage capacitance current-based constant current control,the aforementioned pulse width ΔT(k) according to the capacitancecurrent-based constant current control is used, and in the second-stageinductance current-based constant current control, the aforementionedpulse width ΔT(k) according to the inductance current-based constantcurrent control is used.

If it is assumed that the inductance current-based constant currentcontrol is performed over the entire interval of the step response,there is a possibility of overcurrent occurrence. In order to avoid thisovercurrent, the capacitance current-based constant current control iscombined.

The control mode that is performed by combining the capacitancecurrent-based constant current control and the inductance current-basedconstant current control can avoid occurrence of overcurrent that isexpected by the inductance current-based constant current control. Onthe first stage, the capacitance current-based constant current controlis performed to prevent occurrence of the overcurrent, and after thetiming of no more risk of overcurrent, on the second stage, thecapacitance current-based constant current control is switched to theinductance current-based constant current control, and then, the outputvoltage vo is controlled to follow the control command voltage VREFbeing the target value.

The switching voltage Vc is used to switch the first-stage capacitancecurrent-based constant current control to the second-stage inductancecurrent-based constant current control, so as to prevent the outputvoltage from overshooting the target value, due to current energy storedin the inductance during the capacitance current-based constant currentcontrol.

The control mode shown in FIG. 6 indicates that the inductance currentcontrol is performed subsequent to the capacitance current control. Inthe voltage waveform as shown in FIG. 6(b), voltage V1 indicated by thethin solid line represents the step response when the inductancecurrent-based constant current control is performed over the entireinterval, and the voltage indicated by the thick solid line representsthe step response of the control mode combining the capacitancecurrent-based constant current control and the inductance current-basedconstant current control, including voltage V2 during the capacitancecurrent control and the voltage V3 during the inductance currentcontrol.

In the capacitance current control, the constant current control isperformed on the basis of the command current IC-REF as shown in FIG.6(a), controlling the output voltage vo to follow the target value,while preventing occurrence of overcurrent, and when the output voltagevo reaches the switching voltage Vc that is set to keep the outputvoltage vo from overshooting the target value, the control is switchedto the inductance current-based constant current control. The voltageused in the capacitance current control is indicated as voltage V2.Thereafter, the voltage is controlled to follow the command voltage VREFby the inductance current-based constant current control. The voltageused in the inductance current control is indicated as voltage V3.

(Second Control Mode)

In the control mode combining the capacitance current-based constantcurrent control and the inductance current-based constant currentcontrol, according to the second control mode, two-stage capacitancecurrent-based constant current control is performed, and thereafter theinductance current-based constant current control is performed.

In the control mode as shown in FIG. 7, the two-stage mode isillustrated where subsequent to the capacitance current-based constantcurrent control, the inductance current-based constant current controlis performed. FIG. 7(a) illustrates the command current IC-REF in thecapacitance current-based constant current control, and FIG. 7(b)illustrates voltage waveforms of the output voltage vo. In the voltagewaveforms as shown in FIG. 7(b), voltage V1 indicated by the thin solidline represents the step response when the inductance current-basedconstant current control is performed over the entire interval. In themode combining the capacitance current-based constant current controland the inductance current-based constant current control, the voltageindicated by the thick solid line represents the step response accordingto voltage V2 a when the first-stage capacitance current-based constantcurrent control is performed, voltage V2 b when the second-stagecapacitance current-based constant current control is performed, andvoltage V3 b when the inductance current control is performed. FIG. 7(b)illustrates the state that voltage V1 and voltage V3 b substantiallyoverlap one another when the inductance current-based constant currentcontrol is performed.

In the first-stage capacitance current-based constant current control,on the basis of the command current IC-REF as shown in FIG. 7(a), theconstant current control is performed to control the output voltage voto follow the target value, with preventing occurrence of overcurrent,and when the voltage reaches the switching voltage Vc1 that is definedso as to keep the output voltage vo from overshooting the target value,the control is switched to the second-stage capacitance current-basedconstant current control. The voltage in the first-stage capacitancecurrent-based constant current control is indicated as voltage V2 a, andthe voltage in the second-stage capacitance current-based constantcurrent control is indicated as voltage V2 b.

In the second-stage capacitance current-based constant current control,when the output voltage vo reaches the switching voltage Vc2, thecontrol is switched to the inductance current-based constant currentcontrol. The voltage in the second-stage capacitance current-basedconstant current control is indicated as voltage V2 b.

Thereafter, the voltage is controlled to follow the command voltage VREFby the inductance current-based constant current control. The voltage inthe inductance current-based constant current control is indicated asvoltage V3 b.

The second-stage capacitance current-based constant current controlconnects the first-stage capacitance current-based constant currentcontrol, with the inductance current-based constant current control, andcancels voltage deviation that may occur when the constant currentcontrol is switched. Therefore, this allows the voltage at the time ofstarting the inductance current-based constant current control afterswitched from the capacitance current-based constant current control tobe brought into agreement with theoretical voltage value for the casewhere only the inductance current-based constant current control isperformed over the entire interval without performing the capacitancecurrent control. Accordingly, the switching voltage Vc2 upon switchingfrom the second-stage capacitance current-based constant current controlto the inductance current-based constant current control corresponds tothe switching voltage that is expected to obtain if only the inductancecurrent-based constant current control is performed.

The aforementioned first-stage capacitance current-based constantcurrent control, the second-stage capacitance current-based constantcurrent control, and the inductance current-based constant currentcontrol correspond respectively to the capacitance current-basedconstant current control of mode1 and mode2 described below, and theinductance current-based constant current control of mode3. The commandcurrent and voltage waveforms in FIGS. 6 and 7 are schematically shownfor the illustration purpose, not indicating actual voltage waveforms.

Table 1 shows a relationship between command signals and input signalsof the inductance current-based constant current control and thecapacitance current-based constant current control.

TABLE 1 Constant Current Control Command Signal Input Signal CapacitorCurrent IC-REF Vin ic(k) Vo(k) Inductor Current V-REF ic(k) (Vo(k))

There will now be described the constant current control modes performedby each of the modes; mode1, mode2 and mode3, in one step response. FIG.8 illustrates each of the control modes; mode1, mode2 and mode3. FIG.8(a) illustrates the control mode of mode1, FIG. 8(b) illustrates thecontrol mode of mode2, and FIG. 8(c) illustrates the control mode ofmode3. In the following, descriptions will be provided, taking thethree-phase interleaving control as an example of the multi-phaseinterleaving control.

In the constant current control, the step response is given according tothe multi-stage constant current control including two-stage capacitancecurrent-based constant current control of mode1 and mode2, followed bythe inductance current-based constant current control of mode3.

Mode1:

The constant current control of mode1 corresponds to the first stage ofthe two-stage capacitance current-based constant current control. In themode1-constant current control, the output voltage is prevented fromovershooting the target value, due to current energy stored in theinductance. In the first stage mode1, voltage Vc1 is preset for theswitching to the subsequent second-stage mode2, and mode1 is terminatedwhen the output voltage vo reaches the switching voltage Vc1, and thestage is shifted to mode2.

The pulse width ΔT(k) of mode1 in the three-phase interleaving controlis expressed by:

$\begin{matrix}{{\Delta\;{T(k)}} = \frac{{\frac{L}{3}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right){i_{C}(k)}} + {{Tv}_{O}(k)}}{V_{i\; n}(k)}} & (7)\end{matrix}$

FIG. 8(a) illustrates the mode of mode1-capacitance current-basedconstant current control. The controller receives the input voltage Vin,and feedback of capacitance current ic(k) and output voltage vo(k), toperform the constant current control to follow the command currentIC-REF of the capacitance current.

Mode2:

The mode2-constant current control corresponds to the second stage ofthe two-stage capacitance current-based constant current control. Themode2-constant current control is a transfer mode where the outputvoltage vo achieved according to the mode1-capacitance current-basedconstant current control is shifted to initial voltage from which themode3-inductance current-based constant current control starts.

The capacitance current-based constant current control has a function toprevent overcurrent, but it is not provided with a function to controlthe output voltage to follow the target value. Therefore, control forpreventing the output voltage from overshooting the target value isrequired. After the capacitance current-based constant current controlis performed, the control is switched to the inductance current-basedconstant current control so that the output voltage may not overshootthe target value, but the output voltage vo at the time of switching maybe different from the output voltage vo that is expected to obtain ifthe inductance current-based constant current control is performed overthe entire interval of the step response, and this may cause a deviationtherebetween.

As thus described, in the control mode where switching to the inductancecurrent-based constant current control is performed after thecapacitance current-based constant current control, a deviation mayoccur between the voltage at the time of switching to the inductancecurrent-based constant current control, and the voltage expected toobtain if the inductance current-based constant current control isperformed over the entire interval of the step response. Accordingly,the post-switching inductance current-based constant current control maystart from the voltage different from the output voltage expected toobtain if the inductance current-constant current control is performedover the entire interval.

The two-stage control of the capacitance current-based constant currentcontrol, mode1 and mode2, can cancel the difference in voltage generatedat the time of switching. In this control mode, the capacitancecurrent-based constant current control is configured to have two stages,mode1 and mode2, and deviation of the output voltage that may occur inthe mode1-constant current control can be canceled in mode2, bringingthe voltage value for starting the mode3-inductance current-basedconstant current control into agreement with the output voltage that isexpected to obtain by the inductance current-based constant currentcontrol if it is performed over the entire interval of the stepresponse. With this configuration, the output voltage for starting themode3 inductance current-based constant current control corresponds to atheoretical output voltage value that is obtained if the inductancecurrent-based constant current control is performed over the entireinterval of the step response.

Therefore, the interval of mode2 indicates a transitional interval foradjusting a final value of mode2 to agree with a predetermined value ofmode3, and the constant current control is performed so that the initialvalue of mode2 corresponds to the final value of mode1, and the finalvalue of mode2 corresponds to the initial value Vc2 that is required inmode3.

The pulse width ΔT(k) of mode2 in the three-phase interleaving controlis expressed by:

$\begin{matrix}{{\Delta\;{T(k)}} = \frac{{\frac{L}{3}\beta_{2}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2C}} \right)I_{C\text{-}{REF}}} + {TV}_{C\; 1}}{V_{i\; n}(k)}} & (8)\end{matrix}$

FIG. 8(b) illustrates the control mode of the mode2-capacitancecurrent-based constant current control. The controller performs theconstant current control, to follow the command current β2·IC-REF ofcapacitance current. β2 is a factor for setting the command current inmode2.

Mode3:

In mode3, the output voltage vo is controlled by the inductancecurrent-based constant current control, so that the output voltage vomay not overshoot the target value. If the two-level control of High/Lowis performed, the constant current control is performed so that theoutput voltage may not overshoot or undershoot the target values VH andVL.

The pulse width ΔT(k) of mode3 in the three-phase interleaving controlis expressed by:

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{1}{V_{i\; n}(k)}\frac{L}{3}\left\lfloor {{A_{V}V_{REF}} - {\left( {1 - \beta_{3} - \frac{3T^{2}}{2{LC}}} \right){i_{C}(k)}} + {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}}} \right\rfloor}} & (9)\end{matrix}$Furthermore, when Av is set as Av=3T/L, it is expressed by:

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)L}{3T} - \frac{T}{2C}} \right\}{i_{C}(k)}}}{V_{i\; n}(k)}T}} & (10)\end{matrix}$

FIG. 8(c) illustrates control mode of the mode3-inductance current-basedconstant current control. The controller receives the feedback ofcapacitance current ic(k) and output voltage vo(k), or the feedback ofcapacitance current ic(k), and performs the constant current control tocontrol the output voltage to follow the command voltage VREF. β3 is afactor that is provided to allow the output voltage to stably follow thecommand voltage VREF.

Table 2 below shows a relationship of signals in the mode1 to mode3constant current control modes.

TABLE 2 Constant Current 1st mode of Command Input Factor, Control Inputsignal signal signal Constant mode 1 Capacitor ic IC-REF Vin CurrentiC-REF ic(k) Vo(k) Vo(k) mode 2 Capacitor iC-REF β2 · IC-REF Vin β2Current Vc1 Vc1 β2 mode 3 Inductor V-REF V-REF ic(k) β3 Current ic(Vo(k)) Av Vo(k) β3(Settling to Command Voltage)

There will now be described a settling step to a command voltage,according to the aforementioned mode1 to mode3 steps, with reference tothe flowchart as shown in FIG. 9. The flowchart in FIG. 9 shows each ofthe steps, with the reference symbols P1 to P14.

There are provided settings of command voltage VREF, command currentIC-REF, rated output current IR-rat, and constant current factors αH andαL. In the case of High/Low two-level pulse power control, the commandvoltage of High level is indicated as VH, and the command voltage of Lowlevel is indicated as VL. In addition, αH is a constant current factorof High level in the High/Low two-level pulse power control, and αL is aconstant current factor of Low level in the High/Low two-level pulsepower control (P1).

The switching voltage Vc1 from mode1 to mode2, and the switching voltageVc2 from mode2 to mode3 are calculated. The switching voltages Vc1 andVc2 are calculated according to the formulas 34 and 39 described later(P2).

(Steps of Mode1: P3 to P6)

Initially, the capacitance current-based constant current control isperformed in the steps of mode1.

Values of ic(k) and vo(k) are detected (P3), and the pulse width ΔT(k)of mode1 is calculated. The pulse width ΔT(k) of mode1 is calculatedaccording to formula 7 (formula 24). Formula 24 described below isidentical to formula 7 (P4). On the basis of the pulse width ΔT(k)calculated in P4, the switching operation in the LC chopper circuit iscontrolled to perform the capacitance current-based constant currentcontrol, and then, the output voltage vo(k) is detected (P5).

It is determined whether thus detected output voltage vo(k) reaches theswitching voltage vc1 calculated in P2 (P6). If the output voltage vo(k)has not reached the switching voltage vc1 yet, the steps from P3 to P5are repeated, and when the output voltage vo(k) reaches the switchingvoltage vc1, the operation is shifted to the next mode2 step.

(Steps of Mode2: P7 to P10)

According to the steps of mode2, the capacitance current-based constantcurrent control is performed.

Values of ic(k) and vo(k) are detected (P7), and the pulse width ΔT(k)of mode2 is calculated. The pulse width ΔT(k) of mode2 is calculatedaccording to formula 8 (formula 25). Formula 25 described below isidentical to formula 8 (P8). On the basis of the pulse width ΔT(k)calculated in P8, the switching operation in the LC chopper circuit iscontrolled to perform the capacitance current-based constant currentcontrol, and then, the output voltage vo(k) is detected (P9).

It is determined whether thus detected output voltage vo(k) has reachedthe switching voltage vc2 calculated by P2 (P10). If the output voltagevo(k) has not reached the switching voltage vc2 yet, the steps from P7to P9 are repeated, and when the output voltage(k) reaches the switchingvoltage vc2, the operation is shifted to the next mode3 step.

(Steps of Mode3: P11 to P14)

According to the step of mode3, the inductance current-based constantcurrent control is performed.

Values of ic(k) and vo(k) are detected (P11), and the pulse width ΔT(k)of mode3 is calculated. The pulse width ΔT(k) of mode3 is calculatedaccording to formula 9 (formula 26, formula 28). Formula 26 describedbelow is identical to formula 9 (P12). On the basis of the pulse widthΔT(k) calculated in P12, the switching operation in the LC choppercircuit is controlled to perform the inductance current-based constantcurrent control, and then, the output voltage vo(k) is detected (P13).

It is determined whether Or not thus detected output voltage vo(k) hasreached the command voltage VREF that is provided in the step P1 (P14).If the output voltage vo(k) has not reached the command voltage VREF,the steps from P11 to P13 are repeated, and when the output voltagevo(k) has reached the command voltage VREF, settling to the commandvoltage VREF is completed. When next command voltage VREF is provided,the aforementioned steps from P1 to P14 are repeated for the settling ofthe output voltage vo to the command voltage VREF.

(Derivation of Pulse Width ΔT(k) (Derivation 1 to Derivation 9))

A configuration of the LC chopper circuit as shown in FIG. 10 is anexample of two-way step-down chopper circuit according to themulti-phase interleaving system. In this step-down chopper circuit,wheeling diodes of diodes D1 to D3 employed in a general step-downchopper circuit are replaced by controllable elements to allow excessiveenergy in the output to regenerate on the input side, thereby achievingrapid control from full-load to no-load.

Here, three-phase interleaving is shown as an example of the multi-phaseinterleaving. Three switching circuits constituting the three-phaseinterleaving are provided, and the switching circuits are provided withswitching elements Q1 to Q3 and diodes D1 to D3, respectively. In thephases of the three-phase interleaving, inductance L in the LC circuit 4corresponds to inductances L in each of the three switching circuits,and inductance current values iL1 to iL3 of the respective inductances Lare interleaved phase current values. In the multi-phase interleaving,the LC circuit 4 is provided with one capacitance C, and currentobtained by subtracting the load current iR from the combined current(iL1+iL2+iL3) of the inductance current values iL1 to iL3 passes throughthe capacitance C.

Derivation of the pulse width ΔT(k) will be described in the following.Firstly, an initial stage of the derivation of the pulse width ΔT(k)will be described. On the preceding stage, in the constant currentcontrol for feeding back the combined current of multi-phaseinterleaving as the control current (derivation step 1), state equationsof the two-way step-down chopper circuit of multi-phase interleavingsystem and of the pulse width ΔT(k) are obtained (derivation steps 2 and3), and a function expression of the pulse width ΔT(k) is obtained onthe basis of the state equations (derivation step 4).

Next, with the use of the function expression of the pulse width ΔT(k)obtained for the control current on the preceding stage, there will bedescribed derivation of the pulse width ΔT(k) in the inductancecurrent-based constant current control (derivation step 5), andderivation of the pulse width ΔT(k) in the capacitance current-basedconstant current control (derivation step 6).

Thereafter, there will be described derivation steps (derivation steps 7to 9) for deriving the pulse width ΔT(k) of each of the control modes,mode1, mode2, and mode3, in the control mode where the step response isgiven by the multi-stage constant current control, including two-stagecapacitance current-based constant current control, mode1 and mode2, andthe subsequently performed constant current control of mode3.

Derivation Step 1:

There are derived formulas expressing the control current and outputvoltage in the constant current control that feeds back combined currentas the constant current. FIG. 11 illustrates an equivalent circuit ofthe circuit as shown in FIG. 10, representing the equivalent circuit ina time domain sufficiently longer than the switching frequency, in thefield of automatic closed-loop control response.

In the equivalent circuit as shown in FIG. 11, the combined current(iL1+iL2+iL3=iL) of phase current values of iL1, iL2, and iL3 of therespective phases is represented as a current source, and the combinedinductance of the inductance L of each of the three switching circuitsis represented as (L/3). In this equivalent circuit, the step responseof the output voltage vo according to the input current (iL) receivedfrom the current source is expressed by:

$\begin{matrix}{{{v_{O}(s)} = {{\frac{R}{1 + {sCR}}\frac{i_{L}}{s}} = {{Ri}_{L}\left( {\frac{1}{s} - \frac{1}{s + {1\text{/}{CR}}}} \right)}}}{{v_{O}(t)} = {{Ri}_{L}\left( {1 - e^{{- \frac{1}{CR}}t}} \right)}}} & (11)\end{matrix}$

The formula 11 expresses that the step response of the output voltage voexponentially increases to (R·iL) without inducing secondary oscillatingvoltage.

The time function iL(t) of the combined current of inductance current iLis defined by the following formula 12:i _(L)(t)=i _(C)(t)+i _(R)(t)=A _(V) {V _(REF) −v _(O)(t)}+βi _(C)(t)+i_(R)(t)  (12)

The combined current (iL(t)), the capacitance current ic(t), and theoutput voltage vo(t) are expressed by the following formula 13:

$\begin{matrix}{{{i_{L}(t)} = {{{i_{C}(t)} + {i_{R}(t)}} = {{A_{V}\left\{ {V_{REF} - {v_{O}(t)}} \right\}} + {\beta\;{i_{C}(t)}} + {i_{R}(t)}}}}{{i_{C}(t)} = {{\frac{A_{V}}{1 - \beta}\left\{ {V_{REF} - {v_{O}(t)}} \right\}} = {C\frac{d}{dt}{v_{O}(t)}}}}{{v_{O}(t)} = {V_{REF}\left\{ {1 - e^{{- \frac{A_{V}}{{({1 - \beta})}C}}t}} \right\}}}} & (13)\end{matrix}$

The output voltage vo(t) in the formula 13 indicates that loadresistance R is removed from the output voltage vo(t) expressed by theformula 11, and a final value after lapse of sufficient time (t→∞)converges into the command voltage VREF.

Therefore, by performing the constant current control using the combinedcurrent of inductance current iL(t) expressed by the formula 12 as thecontrol current, the step response control can be performed withoutinducing the secondary oscillating voltage.

In the output voltage vo(t) as expressed by the formula 13, Av is afactor by which a difference value between the output voltage Vo(t) andthe command voltage VREF (VREF−Vo(t)) is multiplied, β is a factor bywhich the capacitance current ic(t) is multiplied, definingfollowability characteristics to the command voltage VREF.

By way of example, as the factor Av approaches “1”, the step responseaffected more strongly by the magnitude of the difference value(VREF−Vo(t)) is given, whereas the factor β approaches “1”, the stepresponse with higher followability to the command voltage VREF is given.

Derivation Step 2:

Next, the state equation of two-way step-down chopper circuit of thethree-phase interleaving system is derived. FIG. 12 illustrates theequivalent circuit of one phase out of three phases. In order to convertthe combined current (iL) expressed by the aforementioned formula 12 toa form as applicable to the constant current control, the state equationof iL (=iL1+iL2+iL3) being the combined current of iL1, iL2, and iL3 asshown in FIG. 10 is obtained, and a relational expression with the pulsewidth ΔT is derived.

According to the ON/OFF operations of Q1/D1 to Q3/D3 per phase in FIG.10, Vin or 0 voltage is applied to U1(τ), U2(τ) and U3(τ). Using theprinciple of superposition, U1(τ) is represented by the equivalentcircuit as shown in FIG. 12. In FIG. 12, U1(τ) is equal to Vin when Q1is ON and D1 is OFF, whereas U1(τ) is equal to 0 when Q1 is OFF and D1is ON.

In the state equation for the circuit of FIG. 10, a general solution ofthe state equation using U(τ) segmented with constant U(t) is expressedby the following formula 14:{dot over (x)}(t)=Ax(t)+Bu(t)x(t)=e ^(At) x(0)+∫₀ ^(t) e ^(A(t-σ)) dσBu(τ)  (14)

The combined current i(t) can be derived from left multiplication of thegeneral solution x(t) by the transformation matrix F corresponding tothe circuit configuration as shown in FIG. 10.

$\begin{matrix}{{{i(t)} = {{{Fx}(t)} = {{{Fe}^{At}{x(0)}} + {F{\int_{0}^{t}{e^{A{({t - \sigma})}}d\;\sigma\;{{Bu}(\tau)}}}}}}}{{where},}} & (15) \\\left. \begin{matrix}\begin{matrix}\begin{matrix}{{{x(t)} = \left\lbrack {{i_{1,1}(t)}\mspace{14mu}{i_{1,2}(t)}\mspace{14mu}{i_{1,3}(t)}\mspace{14mu}{v_{O}(t)}} \right\rbrack^{t}}\mspace{391mu}} \\{{{i(t)} = {\left\lbrack {{i_{1,1}(t)}\mspace{14mu}{i_{1,2}(t)}\mspace{14mu}{i_{1,3}(t)}} \right\rbrack^{t} = {{Fx}(t)}}}\mspace{374mu}}\end{matrix} \\{{{u(\tau)} = \left\lbrack {{u_{1}(\tau)}\mspace{14mu}{u_{2}(\tau)}\mspace{14mu}{u_{3}(\tau)}} \right\rbrack^{t}}\mspace{461mu}}\end{matrix} \\{{F = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0\end{bmatrix}},{A = \begin{bmatrix}0 & 0 & 0 & {{- 1}\text{/}L} \\0 & 0 & 0 & {{- 1}\text{/}L} \\0 & 0 & 0 & {{- 1}/L} \\{1/C} & {1\text{/}C} & {1\text{/}C} & {{- 1}\text{/}{CR}}\end{bmatrix}},{B = {\frac{1}{L}\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & 0\end{bmatrix}}}}\end{matrix} \right\} & (16)\end{matrix}$

In order to obtain the aforementioned iL(t)=iL1(t)+iL2(t)+iL3(t) fromi(t) described above, GFe^(AT) is derived by using the transformationmatrix G. In addition, FB and FAB are transformed as indicated by thefollowing formulas:

$\begin{matrix}\left. \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{{{i_{L}(t)} = {{{i_{L\; 1}(t)} + {i_{L\; 2}(t)} + {i_{L\; 3}(t)}} = {{Gi}(t)}}}\mspace{394mu}} \\{{{G = \left\lbrack {1\mspace{14mu} 1\mspace{14mu} 1} \right\rbrack},{{FB} = {\frac{1}{L}I_{n}}},{{FAB} = 0}}\mspace{419mu}}\end{matrix} \\{{{u_{01} = {V_{in}\left\lbrack {1\mspace{14mu} 0\mspace{14mu} 0} \right\rbrack}^{t}},{u_{02} = {V_{in}\left\lbrack {0\mspace{14mu} 1\mspace{14mu} 0} \right\rbrack}^{t}},{u_{03} = {V_{in}\left\lbrack {0\mspace{14mu} 0\mspace{14mu} 1} \right\rbrack}^{t}}}\mspace{194mu}}\end{matrix} \\{{u_{12} = {V_{in}\left\lbrack {1\mspace{14mu} 1\mspace{14mu} 0} \right\rbrack}^{t}},{u_{13} = {V_{in}\left\lbrack {1\mspace{14mu} 0\mspace{14mu} 1} \right\rbrack}^{t}},{u_{23} = {V_{in}\left\lbrack {0\mspace{14mu} 1\mspace{14mu} 1} \right\rbrack}^{t}},{u_{123} = {V_{in}\left\lbrack {1\mspace{14mu} 1\mspace{14mu} 1} \right\rbrack}^{t}}}\end{matrix} \\{{e^{AT} = {I_{n} + {AT} + \frac{({AT})^{2}}{2}}}\mspace{526mu}}\end{matrix} \\{{{GFe}^{AT} = {{\left( {1 - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right)\left\lbrack {1\mspace{14mu} 1\mspace{14mu} 1\mspace{14mu} 0} \right\rbrack} + {3{\left( {{- \frac{T}{L}} + \frac{T^{2}}{2\mspace{14mu}{LCR}}} \right)\left\lbrack {0\mspace{14mu} 0\mspace{14mu} 0\mspace{14mu} 1} \right\rbrack}}}}\mspace{135mu}}\end{matrix} \right\} & (17)\end{matrix}$Derivation Step 3:

Next, the state equation of the pulse width ΔT(k) is derived.

There will now be obtained the relational expression of the pulse widthΔT(k), in the interval T of one cycle as shown FIG. 2(a). When i(T) isderived by applying the formulas 16 and 17 to the formula 15, the stateequation expressed by the following formula 18 is obtained. Though notshown, i(T) for the interval T of one cycle as shown in each of FIGS.2(b) and 2C is also expressed by the same formula as formula 18:

$\begin{matrix}{{{i(T)} = {{{Fe}^{AT}{x(0)}} + {F{\int_{0}^{t_{2}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{23}}}} + {F{\int_{t_{1}}^{t_{3}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{123}}}} + {F{\int_{t_{2}}^{t_{3}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{13}}}} + {F{\int_{t_{3}}^{t_{4}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{123}}}} + {F{\int_{t_{4}}^{t_{5}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{12}}}} + {F{\int_{t_{5}}^{t_{6}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{123}}}} + {F{\int_{t_{6}}^{t_{7}}{e^{A{({T - \sigma})}}d\;\sigma\;{Bu}_{23}}}}}}{{i(T)} = {{{Fe}^{AT}{x(0)}} + {\frac{1}{L}I_{n}\left\{ {{\left( {T - {\Delta\; T}} \right)\left( {u_{23} + u_{13} + u_{12}} \right)} + {\left( {{{- 2}T} + {3\Delta\; T}} \right)u_{123}}} \right\}}}}\mspace{76mu}{{i(T)} = {{{Fe}^{AT}{x(0)}} + {\frac{\Delta\; T}{L}I_{n}u_{123}}}}} & (18)\end{matrix}$Derivation Step 4:

Next, a function expression of the pulse width ΔT(k) is derived.

When transforming the state equation of the pulse width ΔT(k) of formula18 by using formula 17, following formula is obtained:

$\begin{matrix}{\mspace{76mu}{{{i_{L}(T)} = {{{Gi}(T)} = {{{GFe}^{AT}{x(0)}} + {G\frac{\Delta\; T}{L}I_{n}u_{123}}}}}{{i_{L}(T)} = {{\left( {1 - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right){i_{L}(0)}} + {3\left( {\frac{T^{2}}{2\mspace{14mu}{LCR}} - \frac{T}{L}} \right){v_{O}(0)}} + {\frac{3{V_{in}(k)}}{L}\Delta\; T}}}}} & (19)\end{matrix}$

Assuming the load current iR(k) as iR(k)=vo(k)/R, and removing R fromthe aforementioned formula 19, the following formula 20 is obtained:

$\begin{matrix}{{i_{L}\left( {k + 1} \right)} = {{\left( {1 - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right){i_{L}(k)}} - {\frac{3T}{L}{v_{O}(k)}} + {\frac{3T^{2}}{2\mspace{14mu}{LC}}{i_{R}(k)}} + {\frac{3{V_{in}(k)}}{L}\Delta\;{T(k)}}}} & (20)\end{matrix}$

When the pulse width ΔT(k) is obtained from the aforementioned formula20, following formula is obtained:

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{1}{V_{in}(k)}\left\{ {{\frac{L}{3}{i_{L}\left( {k + 1} \right)}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right){i_{L}(k)}} + {{Tv}_{O}(k)} - {\frac{T^{2}}{2\mspace{14mu} C}{i_{R}(k)}}} \right\}}} & (21)\end{matrix}$

The pulse width ΔT(k) as expressed by the aforementioned formula 21indicates the pulse width ΔT(k) in the inductance current-based constantcurrent control. Hereinafter, on the basis of the formula 21, there willbe described the derivation of the pulse width ΔT(k) in the inductancecurrent control (derivation step 5), and the derivation of pulse widthΔT(k) in the capacitance current control (derivation step 6).

Derivation Step 5:

Next, the pulse width ΔT(k) in the inductance current-based constantcurrent control is derived.

For the pulse width ΔT(k) expressed by the formula 21, the functionexpression is used which is obtained by transforming the inductancecurrent iL expressed as iL(k+1) in formula 12 into a discrete time form,whereby the pulse width ΔT(k) according to the inductance current-basedconstant current control can be obtained. Here, β shown in formula 12 isprovided as β=β3 to be suitable for the mode3-inductance current-basedconstant current control.

$\begin{matrix}\begin{matrix}{{\Delta\;{T(k)}} =} & {\frac{1}{V_{in}(k)}{\frac{L}{3}\begin{bmatrix}{{{A_{V}\left\{ {V_{REF} - {v_{O}(k)}} \right\}} + {\beta_{3}{i_{C}(k)}} +}\mspace{56mu}} \\{{i_{R}(k)} - {\left( {1 - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right)\left\{ {{i_{C}(k)} + {i_{R}(k)}} \right\}} +} \\{{{\frac{3}{L}{{Tv}_{O}(k)}} - {\frac{3T^{2}}{2\mspace{14mu}{LC}}{i_{R}(k)}}}\mspace{135mu}}\end{bmatrix}}} \\{=} & {\frac{1}{V_{in}(k)}{\frac{L}{3}\left\lbrack {{A_{V}V_{REF}} - {\left( {1 - \beta_{3} - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right){i_{C}(k)}} +} \right.}} \\ & \left. {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}} \right\rbrack\end{matrix} & (22)\end{matrix}$

The aforementioned pulse width ΔT(k) is expressed by using thecapacitance current ic(k) and the output voltage vo(k), instead of theinductance current iL(k) in the inductance current-based constantcurrent control. With the expression using the capacitance current ic(k)instead of the inductance current iL(k), the inductance current-basedconstant current control and the capacitance current-based constantcurrent control can be performed by the feedback of common capacitancecurrent ic(k).

Derivation Step 6:

Next, the pulse width ΔT(k) in the capacitance current-based constantcurrent control is derived.

[0172]

In the capacitance current-based constant current control, with thecommand current represented as IC-REF, there is provided a definition ofiL(k+1)=IC-REF+iR(k).

In the pulse width ΔT(k) expressed by formula 21, by usingiL(k+1)=IC-REF+iR(k), the pulse width ΔT(k) in the capacitancecurrent-based constant current control is expressed by the followingformula 23.

$\begin{matrix}\left. \begin{matrix}{{\Delta\;{T(k)}} =} & {\frac{1}{V_{in}(k)}\left\{ {{\frac{L}{3}\left\{ {I_{C\text{-}{REF}} + {i_{R}(k)}} \right\}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right)\left\{ {{i_{C}(k)} + {i_{R}(k)}} \right\}} +} \right.} \\ & \left. {{{Tv}_{O}(k)} - {\frac{T^{2}}{2\mspace{14mu} C}{i_{R}(k)}}} \right\} \\{=} & {\frac{{\frac{L}{3}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right){i_{C}(k)}} + {{Tv}_{O}(k)}}{V_{in}(k)}}\end{matrix} \right\} & (23)\end{matrix}$

According to the aforementioned pulse width ΔT(k), since elements of theload current iR(k) and the inductance current iL(k) are excluded, thepulse width ΔT(k) can be obtained by the feedback of the capacitancecurrent ic(k) and the output voltage vo(k) without feeding back the loadcurrent iR(k) or the inductance current iL(k).

Next, derivation of the pulse width ΔT(k) of capacitance current-basedconstant current control mode1 and mode2, and derivation of the pulsewidth ΔT(k) of inductance current-based constant current control mode3will be described (Derivation step 7 to Derivation step 9).

Derivation Step 7:

Derivation of the pulse width ΔT(k) of the mode1 capacitancecurrent-based constant current control will be described.

In mode1, the first stage of capacitance current-based constant currentcontrol is executed. With the command current represented as IC-REF inthe first stage constant current control, inductance current iL(k+1) isdefined as iL(k+1)=IC-REF+iR(k). By using the pulse width ΔT(k) in theconstant current control using the control current as expressed byformula 21, the pulse width ΔT(k) of mode1 expressed by formula 24 canbe obtained.

$\begin{matrix}\left. \begin{matrix}{{\Delta\;{T(k)}} =} & {\frac{1}{V_{in}(k)}\left\{ {{\frac{L}{3}\left\{ {I_{C\text{-}{REF}} + {i_{R}(k)}} \right\}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right)\left\{ {{i_{C}(k)} + {i_{R}(k)}} \right\}} +} \right.} \\ & \left. {{{Tv}_{O}(k)} - {\frac{T^{2}}{2\mspace{14mu} C}{i_{R}(k)}}} \right\} \\{=} & {\frac{{\frac{L}{3}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right){i_{C}(k)}} + {{Tv}_{O}(k)}}{V_{in}(k)}}\end{matrix} \right\} & (24)\end{matrix}$

Since elements of the load current iR(k) and the inductance currentiL(k) are excluded from the function expression of the pulse width ΔT(k)defining the mode1 control, feedback of the load current iR(k) and theinductance current iL(k) becomes unnecessary.

In the mode1-capacitance current-based constant current control, inorder to prevent the output voltage vo(k) from overshooting the DCcommand voltage VREF within the mode1 period, the first stagemode1-capacitance current-based constant current control is terminatedwhen the output voltage vo(k) reaches Vc1, and it is switched to thesecond stage mode2-capacitance current-based constant current control.Here, Vc1 indicates the output voltage at which mode1 is switched tomode2. In the two-level dead beat control, as the DC command voltage,High DC command voltage VH is defined, and Low DC command voltage VL isdefined.

Derivation Step 8:

Next, derivation of the pulse width ΔT(k) in the mode2-capacitancecurrent-based constant current control will be described.

The mode2 pulse width ΔT(k) is obtained by the following formula 25, bysubstituting vo(k)=Vc1 and iL(k+1)=β2·IC-REF+iR(k), into the generalformula 21 of the pulse width ΔT(k):

$\begin{matrix}\begin{matrix}{{\Delta\;{T(k)}} =} & {\frac{1}{V_{in}(k)}\left\lbrack {{\frac{L}{3}\left\{ {{\beta_{2}I_{C\text{-}{REF}}} + {i_{R}(k)}} \right\}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right)\left\{ {I_{C\text{-}{REF}} + {i_{R}(k)}} \right\}} +} \right.} \\ & \left. {{TV}_{C\; 1} - {\frac{T^{2}}{2\mspace{14mu} C}{i_{R}(k)}}} \right\rbrack \\{=} & {\frac{{\frac{L}{3}\beta_{2}I_{C\text{-}{REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\mspace{14mu} C}} \right)I_{C\text{-}{REF}}} + {TV}_{C\; 1}}{V_{in}(k)}}\end{matrix} & (25)\end{matrix}$

The aforementioned formula 25 is expressed with excluding the elementsof the load current iR(k) and the inductance current iL(k) in thefunction expression of ΔT(k) defining the mode2 control.

In order to achieve rapid response in the constant current control inthe period of mode2, β2 is selected so that the output voltage can reachthe final value Vc2 starting from the initial value Vc1, within oneperiod from the output voltage vo(k) to vo(k+1), whereby mode2 can becompleted within one sampling time.

Derivation Step 9:

Next, derivation of the pulse width ΔT(k) in the mode3-inductancecurrent-based constant current control will be described.

The pulse width ΔT(k) in the mode3-inductance current-based constantcurrent control is similar to the pulse width ΔT(k) in the inductancecurrent-based constant current control described in the derivation step5, and it is expressed by the following formula 26:

$\begin{matrix}\begin{matrix}{{\Delta\;{T(k)}} =} & {\frac{1}{V_{in}(k)}{\frac{L}{3}\begin{bmatrix}{{{A_{V}\left\{ {V_{REF} - {v_{O}(k)}} \right\}} + {\beta_{3}{i_{C}(k)}} +}\mspace{56mu}} \\{{i_{R}(k)} - {\left( {1 - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right)\left\{ {{i_{C}(k)} + {i_{R}(k)}} \right\}} +} \\{{{\frac{3}{L}{{Tv}_{O}(k)}} - {\frac{3T^{2}}{2\mspace{14mu}{LC}}{i_{R}(k)}}}\mspace{135mu}}\end{bmatrix}}} \\{=} & {\frac{1}{V_{in}(k)}{\frac{L}{3}\left\lbrack {{A_{V}V_{REF}} - {\left( {1 - \beta_{3} - \frac{3T^{2}}{2\mspace{14mu}{LC}}} \right){i_{C}(k)}} +} \right.}} \\ & \left. {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}} \right\rbrack\end{matrix} & (26)\end{matrix}$

In general, an AC current transformer for detecting AC signals canprovide rapid response, whereas a commonly used detector for detectingDC signals is relatively slow in response.

The pulse width ΔT(k) expressed in the aforementioned formula detectsthe capacitance current ic(k) and the output voltage vo(k), and usesthem as feedback signals. The capacitance current ic(k) allows rapidresponse according to the AC current transformer, but the response ofthe detector for detecting the output voltage vo(k) is relatively slow.In order to achieve rapid step response, it is necessary to obtainfeedback signals rapidly, and for that purpose, rapid detection by thedetector is desirable.

In light of this situation, there will be described the control wherethe detection of output voltage vo(k) of low-speed response is skipped,and only AC signals of capacitance current are detected rapidly, therebyachieving rapid response.

In the pulse width ΔT(k) as expressed by the aforementioned formula 26,Av is defined as having the relationship expressed by the followingformula 27, thereby eliminating the influence of the output voltagevo(k):Av=3T/L  (27)where T is sampling cycle, and L is inductance of the LC circuit asshown in FIG. 10.

By setting Av as having the relationship of the aforementioned formula27, using the sampling cycle T and inductance L of the LC circuit, thepulse width ΔT(k) can be expressed by the following formula 28 withoutincluding the output voltage vo(k).

$\begin{matrix}{{\Delta\;{T(k)}} = {\frac{V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)L}{3\mspace{14mu} T} - \frac{T}{2\mspace{14mu} C}} \right\}{i_{C}(k)}}}{V_{in}(k)}T}} & (28)\end{matrix}$

The pulse width ΔT(k) expressed by formula 28 includes only thecapacitance current ic(k) as the feedback signal. Since the AC currenttransformer for detecting the capacitance current ic(k) is capable ofproviding rapid response, the pulse width ΔT(k) can be obtained by therapid response.

Accordingly, elements of the output voltage vo(k), the load currentiR(k), and the inductance current iL(k) can be excluded from thefunction expression of the pulse width ΔT(k) that defines themode3-inductance current-based constant current control. Here, β3 isselected in a manner that allows obtainment of a control responsefollowing the DC command voltage VREF, in the constant current controlusing the inductance current iL(t).

(Derivation of Switching Voltage Vc1 and Vc2)

There will now be described derivation of the switching voltage Vc1 forswitching from mode1 to mode2, and derivation of the switching voltageVc2 for switching from mode2 to mode3.

Derivation of Switching Voltage Vc1

Here, in the two-level dead beat control, High DC command voltage VH andLow DC command voltage VL are defined as the DC command voltage VREF.

There will be described the derivation of the switching voltage Vc1, forthe case where target voltage of the step response is High-level commandvoltage VH, and for the case where the target voltage of the stepresponse is Low-level command voltage VL.

(Derivation of Vc1 for Mode1 in High-Level Pulse Control)

Assuming the High-level target voltage is VH, the rated output currentis IR-rat, the constant current factor is αH, and the initial value ofoutput voltage is vo(0), there are established, the command voltageVREF=VH, the command current of capacitance current IC-REF=αH·IR-rat,and the initial value of the output voltage vo(0)=VL.

The mode1-capacitance current-based constant current control correspondsto current control for constant-current charging of the capacitor, andthe output voltage vo(1) to vo(n) at respective points are expressed bythe following formula 29, where the sampling frequency is set to 1, 2, .. . k, . . . n, and more:

$\begin{matrix}{{{v_{O}(1)} = {{\frac{T}{2\mspace{14mu} C}I_{C\text{-}{REF}}} + {v_{O}(0)}}}{{v_{O}(2)} = {{\frac{T}{C}I_{C\text{-}{REF}}} + {v_{O}(1)}}}{{v_{O}\left( {k + 1} \right)} = {{\frac{T}{C}I_{C\text{-}{REF}}} + {v_{O}(k)}}}{{v_{O}(n)} = {{\frac{\left( {n - 0.5} \right)T}{C}I_{C\text{-}{REF}}} + {v_{O}(0)}}}} & (29)\end{matrix}$where k and n are positive integers.

The switching voltage Vc1 is provided for terminating mode1, preventingthe output voltage vo(k) from overshooting the command voltage VREF(=VH) in the period of the mode1-capacitance current-based constantcurrent control. When the output voltage vo(k) reaches the switchingvoltage Vc1, the first stage mode1-capacitance current-based constantcurrent control is terminated, and switching to the second stagemode2-capacitance current-based constant current control is performednext.

In order to prevent the output voltage vo(n) from overshooting theHigh-level command voltage VH, it is necessary to satisfy the relationalexpressions in the following formula 30, in the equivalent circuit asshown in FIG. 11, according to the relationship between the energyaccumulated in the capacitor and input/output energy:

$\begin{matrix}{{{\frac{1}{2} \times \frac{L}{2}I_{C - {REF}}^{2}} \leqq {\frac{1}{2}C\left\{ {V_{H}^{2} - {v_{O}^{2}(n)}} \right\}}}{{v_{O}(n)} \leqq \sqrt{V_{H}^{2} - {\frac{L}{3C}I_{C - {REF}}^{2}}}}} & (30)\end{matrix}$

When these relational expressions 30 are rewritten using the formula 29,the following formula relating to the sampling frequency n can beobtained, which prevents the output voltage vo(n) from overshooting theHigh-level command voltage VH:

$\begin{matrix}{{{{\frac{\left( {n - 0.5} \right)T}{C}I_{C - {REF}}} + {v_{O}(0)}} \leqq \sqrt{V_{H}^{2} - {\frac{L}{3C}I_{C - {REF}}^{2}}}}{n \leqq {{\frac{C}{T}\left\{ {\sqrt{\left( \frac{V_{H}}{I_{C - {REF}}} \right)^{2} - \frac{L}{3C}} - \frac{v_{O}(0)}{I_{C - {REF}}}} \right\}} + 0.5}}{N = {{Int}\left\lbrack {{\frac{C}{T}\left\{ {\sqrt{\left. \frac{\left( V_{H} \right.}{\alpha_{H}I_{R - {rat}}} \right)^{2} - \frac{L}{3C}} - \frac{V_{L}}{\alpha_{H}I_{R - {rat}}}} \right\}} + 0.5} \right\rbrack}}} & (31)\end{matrix}$

Here, N represents a value of integer part of n. Therefore, if thesampling frequency is equal to N or less, the output voltage vo(N) maynot overshoot the High-level command voltage VH.

Assuming the transition voltage for shifting from mode1 to mode2 asVtrans, the output voltage vo(n) expressed by the formula 29 at thesampling frequency N that satisfies the condition of the aforementionedformula 31, may satisfy the following relationship, where VL is theinitial voltage Vo(0) of the output voltage in the High/Low control.

$\begin{matrix}{{{\frac{\left( {N - 1.5} \right)T}{C}\alpha_{H}I_{R - {rat}}} + V_{L}} < V_{trans} \leqq {{\frac{\left( {N - 0.5} \right)T}{C}\alpha_{H}I_{R - {rat}}} + V_{L}}} & (32)\end{matrix}$

When the transition voltage Vtrans is selected by using the average ofthe lowest and highest values in the aforementioned relationalexpression 32, it is expressed by the following formula 33.

$\begin{matrix}{V_{trans} = {{\frac{\left( {N - 1} \right)T}{C}\alpha_{H}I_{R - {rat}}} + V_{L}}} & (33)\end{matrix}$

When the output voltage vo reaches Vc1, equal to higher than thetransition voltage Vtrans that satisfies the formula 33, the control isshifted to mode2. Therefore, the switching voltage Vol in the mode1 inthe High-level pulse control is expressed by the following formula 34:

$\begin{matrix}{V_{C\; 1} = {{\frac{\left( {N - 0.5} \right)T}{C}\alpha_{H}I_{R - {rat}}} + V_{L}}} & (34)\end{matrix}$(Derivation of Vc1 for Mode1 in Low Pulse Control)

There will now be described derivation of Vc1 for mode1 when Low pulsecontrol is performed.

Assuming the Low-level target voltage is VL, the rated output current isIR-rat, the constant current factor is αL, and the initial value of theoutput voltage is vo(0), there are established command voltage VREF=VL,the command current of capacitance current IC-REF=−αL·IR-rat, and theinitial value of the output voltage vo(0)=VH.

In order to prevent the Low-level output voltage vo from undershootingthe target voltage VL, it is necessary to start control from vo(n) andto end the control at the VREF=VL in the formula 29, within the timetus. The time tus corresponds to the time needed until accomplishment ofregeneration to the input voltage Vin in the OFF state of all Q1 to Q3and D1 to D3 in FIG. 10, in other words, it is the time for thecapacitance current is to start from IC-REF until becoming zero current.According to the relational expression of energy in the no load state,it is necessary to satisfy the relationship expressed by the followingformula 35.

$\begin{matrix}{\mspace{79mu}{{{{V_{L} = {{v_{O}(n)} - {\frac{I_{C - {REF}}}{2C}t_{US}}}}\left. {\frac{1}{2} \times \frac{L}{3}I_{C - {REF}}^{2}} \leqq {{V_{in}\frac{I_{C - {REF}}}{2}t_{US}} + {\frac{1}{2}C\left\{ {{v_{O}^{2}(n)} - V_{L}^{2}} \right\}}}\leftrightharpoons{V_{in}\frac{I_{C - {REF}}}{2}t_{US}} \right.} = {{CV}_{in}\left\{ {{v_{O}(n)} - V_{L}} \right\}}}\mspace{79mu}{{v_{O}(n)} \geqq {\frac{{LI}_{C - {REF}}^{2}}{6{CV}_{in}} + V_{L}}}}} & (35)\end{matrix}$

When these relational expressions are rewritten by using the outputvoltage vo(n) in formula 29, the formula 36 that relates to the samplingfrequency n can be obtained, which prevents the output voltage vo(n)from undershooting the Low-level command voltage VL.

$\begin{matrix}{{n \leqq {{\frac{C}{T}\left\{ {\frac{V_{II} - V_{L}}{\alpha_{L}I_{R - {rat}}} - \frac{L\;\alpha_{L}I_{R - {rat}}}{6{CV}_{in}}} \right\}} + 0.5}}{N = {{Int}\left\lbrack {{\frac{C}{T}\left\{ {\frac{V_{II} - V_{L}}{\alpha_{L}I_{R - {rat}}} - \frac{L\;\alpha_{L}I_{R - {rat}}}{6{CV}_{in}}} \right\}} + 0.5} \right\rbrack}}} & (36)\end{matrix}$

Here, N represents a value of integer part of n. If the samplingfrequency is equal to N or less, the output voltage vo(N) may notundershoot the Low-level command voltage VL.

Assuming the transition voltage for shifting from mode1 to mode2 isVtrans, the output voltage vo(n) expressed by the formula 29 satisfiesthe following relationship, at the sampling frequency N that satisfiesthe conditions of the aforementioned formula 36. Here, VL represents theinitial voltage Vo(0) of the output voltage in the High/Low control.

$\begin{matrix}{{V_{H} - {\frac{\left( {N - 0.5} \right)T}{C}\alpha_{L}I_{R - {rat}}}} \leqq V_{trans} < {V_{H} - {\frac{\left( {N - 1.5} \right)T}{C}\alpha_{L}I_{R - {rat}}}}} & (37)\end{matrix}$

Here, using the average of the lowest and highest values of theaforementioned relational expression to select the transition voltageVtrans, it is expressed by the following formula 38:

$\begin{matrix}{V_{trans} = {V_{H} - {\frac{\left( {N - 1} \right)T}{C}\alpha_{L}I_{R - {rat}}}}} & (38)\end{matrix}$

When the output voltage vo(n) reaches Vc1 equal to lower than thetransition voltage Vtrans which satisfies the formula 38, the control isshifted to mode2. Therefore, the switching voltage Vc1 of mode1 in theLow-level pulse control is expressed by the following formula 39:

$\begin{matrix}{V_{C\; 1} = {V_{H} - {\frac{\left( {N - 0.5} \right)T}{C}\alpha_{L}I_{R - {rat}}}}} & (39)\end{matrix}$Derivation of the Switching Voltage Vc2

There will now be described the derivation of the switching voltage Vc2.

In mode2, the second-stage capacitance current-based constant currentcontrol is executed. This second stage mode2-constant current control isto connect the mode1-constant current control and the mode3-constantcurrent control.

If the inductance current-based constant current control is executedover the entire interval of the step response, the output voltage vo(k)operates according to an exponential function as shown in the formula13, and it is expressed by the following formula 40. Here, β in thecapacitance current ic(t) is set as β=β3, using β3 of themode3-inductance current-based constant current control.

$\begin{matrix}{{{v_{O}(t)} = {V_{REF}\left\{ {1 - e^{{- \frac{A_{V}}{{({1 - \beta_{3}})}C}}t}} \right\}}}{{i_{C}(t)} = {{C\frac{d}{dt}{v_{O}(t)}} = {\frac{A_{V}}{1 - \beta_{3}}V_{REF}e^{{- \frac{A_{V}}{{({1 - \beta_{3}})}C}}t}}}}} & (40)\end{matrix}$

The point of the mode2 being the final value agrees with the initialpoint of mode3, and assuming this point as t=t2, the output voltage voand the capacitance current is are expressed by the following formula41:

$\begin{matrix}\left. \begin{matrix}{{v_{O}\left( t_{2} \right)} = {V_{C\; 2} = {{V_{REF} - {V_{REF}e^{{- \frac{A_{V}}{{({1 - \beta_{3}})}C}}t_{2}}}} = {V_{REF} - \frac{i_{C\; 2}\left( {1 - \beta_{3}} \right)}{A_{V}}}}}} \\{{i_{C}\left( t_{2} \right)} = {i_{C\; 2} = {{\frac{A_{V}}{1 - \beta_{3}}V_{REF}e^{{- \frac{A_{V}}{{({1 - \beta_{3}})}C}}t_{2}}} = {\frac{A_{V}}{1 - \beta_{3}}\left( {V_{REF} - V_{C\; 2}} \right)}}}}\end{matrix} \right\} & (41)\end{matrix}$

Vc2 and ic2 are final values of mode2, and simultaneously, they areinitial values of mode3. The switching voltage Vc2 of mode2 is expressedby the formula 42, by using ic2 in the formula 41.

$\begin{matrix}{{V_{C\; 2} = {{V_{C\; 1} + {\frac{I_{C - {REF}} + i_{C\; 2}}{2C}T}} = {V_{C\; 1} + \frac{I_{C - {REF}}T}{2C} + {\frac{A_{V}T}{2{C\left( {1 - \beta_{3}} \right)}}\left( {V_{REF} - V_{C\; 2}} \right)}}}}{V_{C\; 2} = {\frac{T}{{2{C\left( {1 - \beta_{3}} \right)}} + {A_{V}T}}\left\{ {{A_{V}V_{REF}} + {\left( {1 - \beta_{3}} \right)\left( {\frac{2{CV}_{C\; 1}}{T} + I_{C - {REF}}} \right)}} \right\}}}} & (42)\end{matrix}$where VREF=VH, or VREF=VL.(Derivation of Factors β2 and β3)

Next, there will be described the derivation of the factors β2 and β3.

Derivation of the Factor β2:

The control mode of mode2 indicates a transfer mode for the transferfrom mode1 to mode3 with a minimum occurrence of hunting, and in mode2,the initial values are Vc1 and ic1=IC-REF, and the final values are Vc2and ic2.

Under these circumstances, in mode2, control is performed so that thefinal values of mode2 reach the values obtained by formula 41, and thecapacitance current is controlled with the constant current β2·IC-REF,with the setting of β=β2. Here, β2 is a factor to adjust the commandcurrent IC-REF of the capacitance current in mode2.

In other words, the capacitance current ic (k+1) to reach the valueobtained by the formula 41 at the time of (k+1) is expressed by thefollowing formula 43:i _(C)(k+1)=β₂ I _(C-REF) =i _(C2)  (43)

The factor β2 can be obtained by substituting the formula 41 into theformula 43.

$\begin{matrix}{\beta_{2} = {\frac{A_{V}}{1 - \beta_{3}}\frac{V_{REF} - V_{C\; 2}}{I_{C - {REF}}}}} & (44)\end{matrix}$

By setting the factor β2 according to the formula 44, the capacitancecurrent ic can be set as ic2 for the switching time of mode2.

Derivation of Factor β3:

There will be described the derivation of β3 in the mode3 control. β3 isa factor of the capacitance current ic, and it is selected in a mannerthat allows obtainment of the control response following the DC commandvoltage VREF, in the constant current control using inductance currentiL(t).

The factor β3 is selected in a manner that allows obtainment of thecontrol response following the command voltage VREF in the constantcurrent control using inductance-current iL expressed by the formula 12.This selection of factor β3 is performed according to stabilitydetermination in an automatic control system of mode3. Selection of thefactor β3 will be described in the following.

(Closed-Loop First Order Transfer Function of Constant Voltage Control)

Firstly, there will be described a closed-loop first order transferfunction of the constant voltage control. When the inductance currentiL(t) expressed by the formula 12 is represented by S-function with thesetting of β=β3, it is expressed by the following formula 45:

$\begin{matrix}{{i_{C}(s)} = \frac{A_{V}\left\{ {V_{REF} - {v_{O}(s)}} \right\}}{1 - \beta_{3}}} & (45)\end{matrix}$

FIG. 13 illustrates a circuit block of the closed-loop transfer functionas expressed by the aforementioned formula 45, showing the circuit stateaccording to the first order transfer function of the constant voltagecontrol. In the circuit block of the closed-loop transfer function asshown in FIG. 13, control response frequency ωc indicates the pointwhere gain of a loop transfer function reaches “1”. The control responsefrequency ωc that allows the gain of the loop transfer function to reach“1” in FIG. 13 can be obtained according to the following formula 46, bysubstitution of Av of the formula 27.

$\begin{matrix}\left. \begin{matrix}{\omega_{c} = {\frac{A_{V}}{\left( {1 - \beta_{3}} \right)C} = {\frac{3\; T}{\left( {1 - \beta_{3}} \right)L\; C} = \frac{\omega_{n}^{2}T}{1 - \beta_{3}}}}} \\{\omega_{n} = \sqrt{\frac{3}{LC}}}\end{matrix} \right\} & (46)\end{matrix}$

The aforementioned formula 46 indicates that the control responsefrequency ωc is selected based on β3, however, the control responsefrequency ωc to obtain the gain “1” may be affected by the parameters anand T, in addition to β3, and therefore there are restrictions inselecting β3. In light of this situation, a selection range is definedto select the value of β3.

(Closed-Loop Second Order Transfer Function and β3 Selection Range)

Next, there will be described the closed-loop second order transferfunction and β3 selection range.

The formula 28 related to the pulse width ΔT(k) of mode3 is modified andexpressed by a continuous function. Then, the following formula 47 isobtained:

$\begin{matrix}{{{V_{in}(t)}\frac{\Delta\;{T(t)}}{T}} = {{V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)L}{3\; T} - \frac{T}{2\; C}} \right\}{i_{c}(t)}}} = {V_{REF} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)}{A_{V}} - \frac{T}{2\; C}} \right\}{i_{c}(t)}}}}} & (47)\end{matrix}$

The left side member Vin(t)ΔT(t)/T of the aforementioned formula 47represents a mean value of the output voltage vo(t). In other words, inthe circuit as shown in FIG. 10, it corresponds to an average of thevoltage across D1, the voltage across D2, and the voltage across D3.

Therefore, vo(s) representing vo(t) by S-function is expressed as thefollowing, where U=Vin(s)ΔT(s)/T, using the circuit configuration ofFIG. 19,

$\begin{matrix}{{{{{v_{o}(s)} = {{\frac{\omega_{n}^{2}}{s^{2} + {2{ϛ\omega}_{n}s} + \omega_{n}^{2}}\frac{\Delta\;{T(s)}}{T}{V_{in}(s)}} = {\frac{\omega_{n}^{2}}{s^{2} + {2{ϛ\omega}_{n}s} + \omega_{n}^{2}}\left\lbrack {{V_{REF}(s)} - {\left\{ {\frac{\left( {1 - \beta_{3}} \right)}{A_{V}} - \frac{T}{2\; C}} \right\}{i_{c}(s)}}} \right\rbrack}}}\mspace{79mu}\omega_{n}} = \sqrt{\frac{3}{LC}}},{ϛ = {\frac{1}{2\; R}\sqrt{\frac{3}{LC}}}}} & (48)\end{matrix}$

Accordingly, the second order transfer function vo(s)/VREF(s) isillustrated by FIGS. 13 and 14. FIG. 14 shows a circuit state of thesecond order transfer function of the constant voltage control. The looptransfer function of vo(s) in FIG. 14 is expressed by the followingformula 49:

$\begin{matrix}{{\frac{A_{V}}{1 - \beta_{3}}{e^{- T_{n}}}\left( {\frac{1 - \beta_{3}}{A_{V}} - \frac{T}{2\; C}} \right){\frac{\omega_{n}^{2}}{s^{2} + {2{ϛ\omega}_{n}s} + \omega_{n}^{2}}}} = {\left\{ {1 - \frac{A_{V}T}{2\left( {1 - \beta_{3}} \right)C}} \right\}{\frac{\omega_{n}^{2}}{s^{2} + {2{ϛ\omega}_{n}s} + \omega_{n}^{2}}}{e^{- T_{s}}}}} & (49)\end{matrix}$

Since this transfer function indicates positive feedback, the gain inthe control response should be selected as “1” or less, so as to avoidoscillation. According to this restriction imposed on the gain, thefollowing conditional expression 50 is obtained:

$\begin{matrix}{{\left\{ {1 - \frac{A_{V}T}{2\left( {1 - \beta_{3}} \right)C}} \right\}{\frac{\omega_{n}^{2}}{\left( {j\;\omega_{C}} \right)^{2} + {2{Ϛ\omega}_{n}j\;\omega_{C}} + \omega_{n}^{2}}}} < 1} & (50)\end{matrix}$

In this conditional expression 50, assuming the factor represented byword-final sigma as zero, there will be considered the case where thestability condition becomes the worst. Substitution of the formula 46into this conditional expression yields the following formula 51:

$\begin{matrix}{{{\left( {1 - \frac{\omega_{c}T}{2}} \right){\frac{\omega_{n}^{2}}{- \left( {\omega_{C}^{2} - \omega_{n}^{2}} \right)}}} = {{\left( {1 - \frac{\omega_{c}T}{2}} \right)\frac{\omega_{n}^{2}}{\omega_{C}^{2} - \omega_{n}^{2}}} < 1}}{\omega_{C} > {\omega_{n}\left\{ {\sqrt{2 + \left( \frac{\omega_{n}T}{4} \right)^{2}} - \frac{\omega_{n}T}{4}} \right\}}}} & (51)\end{matrix}$

In determining the stability, the control response frequency ωc isrestricted by the aforementioned conditional expression, and inaddition, impact imposed by dead time in the switching time T will beconsidered.

The dead time is expressed by exp(−jωcT)=cos(ωcT)−j cos(ωcT). Therefore,the range of cc is defined as ωc<π/(2T), which permits the phase marginof the loop transfer function of vo(s) as shown in FIG. 13 is up to0[deg], that is, ωcT=π/2.

By using the formula 46, the range of (1−β3) is expressed by thefollowing formula 52:

$\begin{matrix}{{1 - \beta_{3}} > \frac{2\omega_{n}^{2}T^{2}}{\pi}} & (52)\end{matrix}$

The range of (1−β3) including formula 51 is expressed by the formula 53,and this allows selection of the factor β3:

$\begin{matrix}{\frac{2\omega_{n}^{2}T^{2}}{\pi} < {1 - \beta_{3}} < \frac{\omega_{n}T}{\sqrt{2 + \left( \frac{\omega_{n}T}{4} \right)^{2}} - \frac{\omega_{n}T}{4}}} & (53)\end{matrix}$

In the constant current control using the inductance current iL(t), thefactor β3 is selected from the range as described above, and the gain isreduced to be equal to or less than “1”, allowing the control responseto stably follow the DC command voltage VREF.

(Detection of Output Voltage Vo(t))

There will now be described rapid detection of the output voltage vo(t).

In order to perform control with high switching frequency, it isnecessary to detect the output voltage vo(t) and the capacitance currentic(t) rapidly. In the pulse control including two levels of High/Low, inparticular, in the mode1 and mode2 capacitance current-based constantcurrent control, detectors for detecting the output voltage vo(t) andthe capacitance current ic(t) are required to perform rapid measurement.

In order to detect the output voltage vo(t) rapidly, detection signalVo-slow is used as an initial value vo(0), which is detected by adetection means with relatively slow response characteristics like acommonly-used sensor. Then, the initial value vo(0) and the capacitancecurrent ic(t) are subjected to rapid discrete time process, and then theoutput voltage vo(t) is obtained. In acquiring the output voltage vo(t),the detection signal Vo-slow detected by the detection means with therelatively slow response characteristics, is set as the initial valuevo(0). However, only the initial value vo(0) is a detection target bythe detection means, and the output voltage vo(t) at each point of timecan be computed, without using the detection means that is slow in theresponse speed. Accordingly, this allows rapid detection.

In mode3, the output voltage vo(t) at each point t can be obtainedwithout usage as a feedback signal, and thus, there is no impact ofdisturbance due to vo-slow. Therefore, vo-slow is provided in thesettling interval in mode3. In the mode1 to mode3 constant currentcontrol performed in each sampling cycle, the final value vo-slow ofmode3 in the previous sampling cycle, is used as the initial value vo(0)for obtaining vo(t) to be used in mode1 and mode2 in the subsequentsampling cycle.

In the step-down chopper circuit example of the three-phase interleavingsystem as shown in FIG. 1, the sampling time T is set as T=1/Fs, whereFs is the switching frequency.

In order to detect the output voltage vo(t) rapidly, sampling time Th isprovided, sufficiently shorter than the sampling time T, satisfyingTh<0.1·(T/3).

In this sampling time Th, capacitance current ic(t) is detected by an ACtransformer that allows rapid detection easily, and then, followingdiscrete time process is performed thereon. Here, Th is defined asTh=tm−tm−1.

$\begin{matrix}{{{V_{O\text{-}\det}\left( k_{m} \right)} = {{\frac{1}{C}{\int_{t_{m - 1}}^{t_{m}}{{i_{C}(t)}d\; t}}} + {V_{O\text{-}\det}\left( {k_{m} - 1} \right)}}}{{V_{O\text{-}\det}\left( k_{m} \right)} = {{\frac{i_{C}\left( {k_{m} - 1} \right)}{C}T_{h}} + {V_{O\text{-}\det}\left( {k_{m} - 1} \right)}}}} & (54)\end{matrix}$

In the two-level pulse control where two-level High/Low pulse operationis performed in wideband (1 Hz to 50 Hz), after the settling of the Low(High) level, the next output voltage is used as an initial valuevoltage of High (Low) of the next High/Low two-level pulse operation.

After settling of the Low level pulse operation, the High level pulseoperation starts from the output voltage VL. If the output voltagereaches VH after the settling, the following formula 55 is established:

$\begin{matrix}\left. \begin{matrix}{{v_{O}(1)} = {{\frac{i_{C}(0)}{C}T_{h}} + {v_{O}(0)}}} \\{{v_{O}(2)} = {{\frac{i_{C}(1)}{C}T_{h}} + {v_{O}(1)}}} \\{{v_{O}(3)} = {{\frac{i_{C}(2)}{C}T_{h}} + {v_{O}(2)}}} \\{{v_{O}\left( k_{m} \right)} = {{\frac{i_{C}(2)}{C}T_{h}} + {v_{O}\left( {k_{m} - 1} \right)}}}\end{matrix} \right\} & (55)\end{matrix}$

In formula 55 above, the detection signal vo-slow obtained by thedetection means like a commonly-used sensor, with relatively slowresponse, can be used as the initial value vo(0) corresponding to VL.

The control of mode3 still continues even after the output voltagevo(km) reaches the set voltage VH-set. Assuming the VH-set arrival timeas Tset, the relationship as the following is established between thesampling frequency km and Tset in mode1 and mode2 and Tset:km·Th>Tsetkm>Tset/Th

In practical applications, in the case where Tset=8 μs and Th= 1/60 MHz,km>8 μs×60 MHz=480. In this example, resolution of 480 or higher can beobtained, and the detection speed is Th= 1/60 MHz=0.0167 μs.

Similarly, Low level pulse operation starts from voltage VH after thesettling of the High level pulse operation, and when reaching thevoltage VL after the settling, it becomes possible to use the detectionsignal vo-slow as vo(0) corresponding to VH, which is obtained throughdetection by the commonly-used sensor relatively slow in response. Thecontrol of mode3 still continues even after vo(km) reaches the setvoltage VL-set.

The power supply device of the present invention is applicable to adouble control system of two-level dead beat control, including a mainloop that follows a command signal from the power supply device, and aminor loop that follows High/Low DC command voltage of the two-waystep-down chopper circuit of the multi-phase interleaving system, andthis invention is applicable to devices such as a DC power supplydevice, an AC power supply device including an UPS, and an RF generator.

With reference to FIG. 15, an example where the power supply device ofthe present invention is applied to the RF generator will be described,an operation example will be described when the power supply device ofthe present invention is applied to the RF generator with reference tothe flowchart of FIG. 16, and with reference to the flowchart of FIG.17, a High/Low control example will be described. In addition, withreference to FIG. 18, there will be described an example where the powersupply device of the present invention is applied to a DC power supplydevice and to an AC power supply device.

(Application Example of RF Generator)

FIG. 15 is a control block diagram illustrating a control system as anapplication example of the RF generator. The control system comprises PIcontrol constituting a main loop control system, and a dead beat controlconstituting the minor loop control system. Here, two-level dead beatcontrol system of the power supply device according to the presentinvention is applied to the dead beat control constituting the minorloop control system. This two-level dead beat control system isconfigured to follow High/Low DC command voltage in the two-waystep-down chopper circuit of multi-phase interleaving system.

When performing the two-level control of High-level and Low-level, inthe main loop, High-level forward wave power command PH-Forward, orHigh-level load power command PH-Load is used as a High-level commandsignal, and Low-level forward wave power command PL-Forward, orLow-level load power command PL-Load is used as a Low-level commandsignal. Then, the PI control is performed by feeding back the High-levelforward wave power or the Low-level forward wave power, or theHigh-level load power or the Low-level load power, acquired from theload side. As rated values, rated DC voltage Vo-rat, rated DC currentIo-rat, and rated forward wave power Ph-rat are inputted.

On the other hand, in the minor loop, the High-level command voltage VHand the Low-level command voltage VL obtained by the PI control are setas command values, and the dead beat control is performed by feedingback the output voltage vo or the capacitance current ic.

The flowchart in FIG. 16 shows a startup mode for the RF generator toignite plasma in a plasma load. In the flowcharts as shown in FIGS. 16and 17, steps are labeled with the reference symbols such as S1 to S10,and S11 and S12, respectively.

There are provided rated values of the RF generator, and command valuesfor driving the RF generator. As the rated values, rated DC voltageVo-rat, rated DC current Io-rat, and rated forward wave power PH-rat areprovided and they are inputted to set the rated values. In addition, asa High-level power command PH, the High-level forward wave power commandPH-Forward, or the High-level load power command PH-Load is inputted,and as a Low-level power command PL, the Low-level forward wave powercommand PL-Forward or the Low-level load power command PL-Load isprovided (S1).

Initially, ramp-up operation is performed with continuous mode up to theHigh-level power command PH, for example, in 20 ms (Ramp Up (PH-rat/20ms)) (S2).

If plasma is not ignited according to voltage rise with the continuousmode (S3), igniting operation is performed according to prepulsecontrol. The prepulse control is to apply more than one prepulse with apulse width narrower than a main pulse, thereby forming an atmosphere ofplasma ignition, as a preceding stage prior to applying the main pulsethat induces plasma ignition. Patent Document 4 discloses this prepulsecontrol.

In the prepulse control, according to the duty control at 5 kHz, forexample, supplied power is raised to PH, with maintaining the averagereflected power PREF-ave to a predetermined value. The predeterminedvalue of the average reflected power PREF-ave is defined by multiplyingthe High-level rated power PH-rat by a predetermined factor, forinstance. By way of example, 0.1 may be set as the predetermined factor.A pulse under ON/OFF control at a duty ratio of 10% may be used as thisaverage reflected power PREF-ave of the prepulse mode.

A patterned operation of the prepulse mode is repeated, and when therepetitive operation count reaches a prescribed number of times, failureof ignition is displayed, and the operation is suspended (S4).

When plasma is ignited (S3), a High-level voltage value VH is reserved,which starts from the High-level power command PH set at High level andafter settling to the High-level power command PH (S5).

Then, according to ramp down operation (Ramp Down (PH-rat/20 ms)),dropping from the High-level power command PH to the Low-level powercommand PL is performed (S6), the Low-level voltage value VL after thesettling to the Low-level power command PL is reserved (S7).Accordingly, High-level command voltage VH after the settling can be setas the High-level command voltage VREF (High), that is, VREF(High)=VH,and the Low-level command voltage VL after the settling can be set asthe Low-level command voltage VREF (Low), that is, VREF(Low)=VL.

Thereafter, if arc is generated, after suspending the power supply byarc interruption control, the ignition operations from S2 to S7 areperformed (S8), whereas if arc interruption control is not performed,the High/Low two-level control is performed (S10).

(High/Low-Level Control)

Next, with reference to the flowchart of FIG. 17, an example of theHigh/Low-level control will be described. In the flowchart of FIG. 17,the High/Low-level control includes, the PI control according to themain loop (S11) where output power is made to follow the power commandof the forward wave power PH(Forward)/PL(Forward), or the power commandof load power PH (Load)/PL (Load), and the dead beat control accordingto the minor loop (S12) where the output voltage is made to follow theHigh/Low two-level command voltage.

In the PI control using PH and PL according to the main loop of S11,processing is performed in a sampling cycle Tc slower than the samplingcycle T in which the dead beat control of the minor loop is performed(S11A). For example, the sampling cycle Tc may be 50 μs, and the H/Lpulse cycle may be set to 1 Hz to 50 kHz.

In the minor loop control (S12) performed during the process of PIcontrol of S11A, if it is performed according to three-phaseinterleaving, for example, the output voltage vo(km) using the samplingcycle Th is computed according to the following formula 56 included inthe formula (55):vo(km)=(ic(km−1)/C)·Th+vo(km−1)  (56)As to each phase in the three-phase interleaving, vo(km) obtained inevery T/3, being one-third of the sampling cycle T, is detected as theoutput voltage vo(k).

Here, km represents resolution, and km>Tset/Th=8 μs×60 MHz=480 in thecase where Tset=8 μs and Th= 1/60 MHz, for example. In this example, theresolution of 480 or higher can be obtained (S12A).

Then, the High-level command voltage VH and the Low-level commandvoltage VL are acquired (S12B), and each of vo(km) at k point after thesettling is acquired as the High-level output voltage vo(k) and as theLow-level output voltage vo(k) (S12C).

The High-level pulse width ΔT(k) is obtained (S12D), and by using thusobtained pulse width ΔT(k), the output voltage vo is controlled tofollow the High-level command voltage VH. Next, the Low-level pulsewidth ΔT(k) is obtained (S12E), and by using thus obtained pulse widthΔT(k), the output voltage vo is controlled to follow the Low-levelcommand voltage VL.

Starting from the control to follow the High-level power command PH, thecontrol to follow the Low-level power command PL is performed next. TheHigh-level PH control and the Low-level PL control are repeated, andoperation of the High/Low pulse power control continues.

Every time each High/Low pulse power control is finished, peak holdingis performed to hold data of; High-level end power PH-end and Low-levelend power PL-end, and High-level end voltage VH-end and Low-level endvoltage VL-end.

The High-level end voltage VH-end and Low-level end voltage VL-end areheld as the command voltage VH and VL, the command voltage VREF in theformula 12 in association with the High/Low levels, respectively. Inaddition, the High-level end power PH-end and the Low-level end powerPL-end are used as feedback signals of High/Low pulses.

(Application Examples of DC Power Supply Device and AC Power SupplyDevice)

Next, with reference to FIG. 18, there will be described the exampleswhere the power supply device of the present invention is applied to aDC power supply device and to an AC power supply device.

FIG. 18 is a control block diagram illustrating a control system of theapplication example where the power supply device of the presentinvention is applied to the DC power supply device and to the AC powersupply device. The control system comprises the PI control constitutingthe main loop control system, and the dead beat control constituting theminor loop control system. The two-level dead beat control system of thepower supply device according to the present invention is applied to thedead beat control constituting the minor loop control. The two-leveldead beat control system follows High/Low DC command voltage of thetwo-way step-down chopper circuit in the multi-phase interleavingsystem.

When two-level control; High-level and Low-level, is performed,High-level power command PH or High-level voltage command VrefH, andLow-level power command PL or Low-level voltage command VrefL, are usedas command signals in the main loop, and power or voltage acquired fromthe load side is fed back, whereby PI control is performed. As ratedvalues, rated DC voltage Vo-rat, rated DC current Io-rat, and ratedforward wave power PH-rat are inputted.

On the other hand, in the minor loop, High-level command voltage VH andLow-level command voltage VL obtained by the PI control are used ascommand values, the dead beat control is performed by feeding back theoutput voltage vo or capacitance current ic.

The embodiments and modifications described above are just examples ofthe power supply device of the present invention. Therefore, it is to beunderstood that the present invention is not limited to each of thoseembodiments, but it may be variously modified on the basis of the spiritof the present invention, and such modifications are not excluded fromthe scope of the invention.

INDUSTRIAL APPLICABILITY

The power supply device of the present invention may be applicable tosupplying of RF power, to devices utilizing radio frequency, such asequipment for manufacturing a semiconductor, a liquid crystal panel, orthe like, vacuum deposition equipment, and heating and meltingequipment.

DESCRIPTION OF SYMBOLS

-   1 power supply-   2 chopper circuit-   3 switching circuit-   4 LC circuit-   5 switching signal generator-   6 controller-   7 load-   Av, β factor-   C capacitance-   D1-D3 diode-   F transformation matrix-   G transformation matrix-   IC-REF command current of capacitance current-   IR-rat rated output current-   Io-rat rated DC current-   ic capacitance current-   iL inductance current-   iL1-iLn inductance current-   iR load current-   L inductance-   N sampling frequency-   PH High-level power command-   PH-Forward High-level forward wave power command-   PH-Load High-level load power command-   PH-end High-level end power-   PH-rat High-level rated power-   PL Low-level power command-   PL-Forward Low-level forward wave power command-   PL-Load Low-level load power command-   PL-end Low-level end power-   PREF-ave average reflected power-   Q1-Q3 switching element-   R load-   T sampling cycle-   Th sampling time-   Tc sampling cycle-   V input voltage-   Vc1 switching voltage-   Vc2 switching voltage-   VH High-level command voltage-   VH-end High-level end voltage-   VH-set High-level set voltage-   VL Low-level command voltage-   VL-end Low-level end voltage-   VREF command voltage-   Vin input voltage-   V1 set voltage-   vo output voltage-   Vo-rat rated DC voltage-   Vo-slow detection signal-   Vtrans transition voltage-   km sampling frequency-   vo output voltage-   ΔT(k) pulse width

What is claimed is:
 1. A power supply device including an LC choppercircuit, comprising, a controller configured to perform step responsecontrol to allow an output voltage or a capacitance current in the LCchopper circuit to follow a plurality of command values, according tomulti-phase interleaving control for performing multi-phase controlusing a plurality of phase current values, and a switching signalgenerator configured to generate a switching signal, wherein, thecontroller performs a computation of a pulse width ΔT(k) of theswitching signal in every sampling cycle T, the switching signal drivingthe LC chopper circuit according to constant current control in apredetermined cycle, the constant current control being performed basedon control current including combined current, the combined currentbeing obtained by combining phase current values in the LC choppercircuit, each of the plurality of command values being command currentof each current of a capacitance and/or command voltage of each voltageof the output voltage in the LC chopper circuit, and the switchingsignal generator generates the switching signal per phase, using thepulse width ΔT(k) computed by the controller as the pulse width ΔT(k)per phase current.
 2. The power supply device according to claim 1,wherein, the control current is combined current of inductance currentvalues of respective phases in an LC circuit, and/or the capacitancecurrent.
 3. A method for controlling a power supply device including anLC chopper circuit, the method performing step response control to allowan output voltage or a capacitance current in the LC chopper circuit tofollow a plurality of command values according to multi-phaseinterleaving control to perform multi-phase control using a plurality ofphase current values, comprising the steps of, controlling forcomputation of a pulse width ΔT(k) of a switching signal in everysampling cycle T, the switching signal driving the LC chopper circuitaccording to constant current control in a predetermined cycle, theconstant current control being performed based on control currentincluding combined current, the combined current being obtained bycombining phase current values in the LC chopper circuit, each of theplurality of command values being command current of each current of acapacitance and/or command voltage of the combined current of inductancecurrent values in the LC chopper circuit, and generating the switchingsignal per phase, using the pulse width ΔT(k) thus computed as the pulsewidth ΔT(k) per phase current.
 4. The method for controlling the powersupply device according to claim 3, wherein, the control current is thecombined current of the inductance current values of respective phasesin an LC circuit, and/or the capacitance current.
 5. The method forcontrolling the power supply device according to claim 4, wherein, thecontrol current includes the combined current of the inductance currentvalues of respective phases in the LC circuit, on the basis of thecontrol current, the constant current control using the inductancecurrent or the constant current control using the capacitance current isperformed, and the pulse width ΔT(k) according to three-phaseinterleaving control in the multi-phase interleaving control isexpressed by:${\Delta\;{T(k)}} = {\frac{1}{V_{in}(k)}\left\{ {{\frac{L}{3}{i_{L}\left( {k + 1} \right)}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\; C}} \right){i_{L}(k)}} + {T\;{v_{O}(k)}} - {\frac{T^{2}}{2\; C}{i_{R}(k)}}} \right\}}$where Vin(k) is input voltage, vo(k) is the output voltage, iL(k) is thecombined current of the inductance current values of respective phases,iR(k) is load current, L is inductance of the LC circuit, C is thecapacitance of the LC circuit, and T is one sampling cycle period. 6.The method for controlling the power supply device according to claim 4,wherein, the control current is the capacitance current in the LCcircuit, the constant current control is performed based on thecapacitance current, and the pulse width ΔT(k) according to three-phaseinterleaving control in the multi-phase interleaving control isexpressed by:${\Delta\;{T(k)}} = \frac{{\frac{L}{3}I_{C - {REF}}} - {\left( {\frac{L}{3} - \frac{T^{2}}{2\; C}} \right){i_{C}(k)}} + {T\;{v_{O}(k)}}}{V_{in}(k)}$where Vin(k) is input voltage, vo(k) is the output voltage, ic(k) is thecapacitance current, IC-REF is capacitance command current, L isinductance of the LC circuit, C is the capacitance of the LC circuit,and T is one sampling cycle period.
 7. The method for controlling thepower supply device according to claim 4, wherein, the control currentis the capacitance current in the LC circuit, the constant currentcontrol is performed based on the capacitance current, and the pulsewidth ΔT(k) according to three-phase interleaving control in themulti-phase interleaving control is expressed by:${\Delta\;{T(k)}} = \frac{{\begin{matrix}L \\3\end{matrix}\beta_{2}I_{C - {REF}}} - {\left( {\begin{matrix}L \\3\end{matrix} - \frac{T^{2}}{2\; C}} \right)I_{C - {REF}}} + {TV}_{C\; 1}}{V_{in}(k)}$where Vin(k) is input voltage, IC-REF is capacitance command current, β2is a factor of capacitance command current, L is inductance of the LCcircuit, C is the capacitance of the LC circuit, T is one sampling cycleperiod, and V_(C1) is initial value of the output voltage.
 8. The methodfor controlling the power supply device according to claim 4, wherein,the control current is the inductance current in the LC circuit, theconstant current control is performed based on the inductance current,and the pulse width ΔT(k) according to three-phase interleaving controlin the multi-phase interleaving control is expressed by:${\Delta\;{T(k)}} = {\frac{1}{V_{in}(k)}{\frac{L}{3}\left\lbrack {{A_{V}V_{REF}} - {\left( {1 - {\beta_{3}\frac{3T^{2}}{2\;{LC}}}} \right){i_{C}(k)}} + {\left( {{\frac{3}{L}T} - A_{V}} \right){v_{O}(k)}}} \right\rbrack}}$where Vin(k) is input voltage, VREF is command voltage, vo(k) is theoutput voltage, ic(k) is the capacitance current, β3 is a factor of thecapacitance current, L is inductance of the LC circuit, C is thecapacitance of the LC circuit, T is one cycle period, and A_(v) is afactor by which a difference between the command voltage VREF and theoutput voltage vo(k) is multiplied.
 9. The method for controlling thepower supply device according to claim 8, wherein, Av is defined asAv=3T/L, and the pulse width ΔT(k) according to three-phase interleavingcontrol in the multi-phase interleaving control is expressed by:${\Delta\;{T(k)}} = {\frac{V_{REF} - {\left\{ {\begin{matrix}{\left( {1 - \beta_{3}} \right)L} \\{3\; T}\end{matrix} - \begin{matrix}T \\{2\; C}\end{matrix}} \right\}{i_{C}(k)}}}{V_{in}(k)}T}$ where Vin(k) is inputvoltage, VREF is command voltage, ic(k) is the capacitance current, β3is a factor of the capacitance current, L is inductance of the LCcircuit, C is the capacitance of the LC circuit, and T is one cycleperiod.